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ENGINEERING WORKSHOP 



ERNEST PULL 




,- , i~»W' i '~ 





ENGINEERING WORKSHOP 
MANUAL 



BY THE SAME AUTHOR 
Crown 8vo, cloth. Price 2s. Gel. net. 

gCREW CUTTING FOR ENGINEERS. A 

Handbook for Practical Mechanics and Technical 
Engineers. 92 pp., with 48 illustrations. 



Crovm 8-vo, cloth. Price 4s. 6d. net. 

J^ODERN ENGINEERING MEASURING 
TOOLS, A Handbook on Measuring and Precision 
Tools as used in the Modern Tool Room and Engineering 
Workshop. 120 pp., 1 10 illustrations and many tables. 



Waistcoat Pocket Size, limp. Price 2s. 6d. net. 

ENGINEERING WORKSHOP NOTES AND 
DATA. A selection of Practical Notes, Formulae 
and Data based on Modern Methods and applicable to all 
branches of Engineering Workshop Practice. 1 28 pp. 



Thb Technical Pbess Ltd. 



ENGINEERING WORKSHOP 
MANUAL 

FOR 

FITTERS, TURNERS, AND GENEIIAL MACHINISTS 

CONTAINING 

PRACTICAL INFORMATION ON THE MIOBOMBTBB, 

VERNIER, TOOLS, SCREW-CUTTING, WORKSHOP 
ARITHMETIC, GEOMETRY, MENSURATION, GEAR- 
CUTTING, PRECISION GRINDING, AND GENERAL 
MACHINE WORK. WITH NOTES, RULES, AND 
TABLES 

BY 

ERNEST PULL 

R.N.R. M.I.MECH.E., M.I.MAR.E. 

AUTHOR OP "MODERN WORKSHOP PRACTICE ", " MODERN MILLING ", 

" KCRKW-CDTTINO FOR ENGINP.EU8 ", ETC 

CHIEF INSTRUCTOR AND LECTURER AT THE LONDON COUNTY 

COUNCIL SCHOOL OF ENGINEERING, POPLAR. LONDON, K. 14 

Mill; 140 ailustrrttions mb mnnjr ®nblcs 

SIXTH EDITION 
REVISED AND ENLARGED OF 
" Tu la Enqineerinq Workshop Handbook" 
Ninth Impression. 



LONDON: 
THE TECHNICAL PRESS LTD. 

6 AVE MARIA LANE, LTJDGATE HILL, E.C.4. 
1938 



NOTICE 

A PPRENTICES AND MECHANICS desiring a 
more advanced book on Engineering Workshop 
Practice should obtain " WORKSHOP PRACTICE ", 
a Practical Textbook, a Revised and Enlarged 
edition of E. PulPa "Modern Workshop Practice". 
New Edition by F. Johnstone Taylor containing 
780 pages, 542 illustrations. Just Published. Net. 16s. 

An up-to-date book written in a plain, concise 
manner. Recommended by the University of 
London, the London County Council, and many 
important Educational Authorities. 



This Technical Press Ltd. 



PREFACE TO SIXTH EDITION 



The object of this book is to provide in as small a space 
as possible practical information that should be known by 
all apprentices, improvers, and journeymen engaged in 
engineering workshops. 

It frequently happens that the book giving the desired 
information is not available at the moment it is required, or 
the data is diffioult to find. A book of this size can be con- 
veniently carried in the pocket, and is likely to be at hand when 
wanted. 

The various chapters have been revised, and the information 
given will be found up-to-date and reliable. 

It is understood that the London County Council accepts 
no responsibility for any opinions or conclusions appearing 
in the book. 

The author would be glad to receive any criticism, or answer 
any questions relating to the matter appearing in the book. 

E. P. 

London County Council 
School of Engineering, 

High Street, Poplar, E. 14. 



JUST PUBLISHED 

ELEMENTS OF PRACTICAL FLYING 

A survey for Students and Pilots. By P. W. F. 

Mill8. 140 pages. Illustrated. Net 4s. 6d. 

" The principles of flight and the functions of the 
various controls of an aeroplane are described in 
simple language with the aid of diagrams." — 
Institute of Transport. 

" The popularization of flying makes this present 
introduction to the subject very welcome."— Library 
World, 

"... Mr. Mills deals with the whole subject in 
a concise and erudite manner." — Flight 



The Technical Press Ltd. 



CONTENTS. 



riUi'TKii 


P*OK 


I. 


Workshop Arithmetic 


1 


II. 


Mensuration and Geometky 


22 


III. 


Materials 


34 


IV. 


IIeat Treatment of Metals 


46 


V. 


Common Workshop Tools . 


50 


VI. 


Measuring Tools and Gauges . 


56 


VII. 


Lathe Work and Turning . 


67 


VIII. 




78 


IX. 




94 


X. 


Drilling, Tapping, and Screwing . 


112 


XI. 


Bench-work 


118 


XII. 


Planing and Shaping .... 


123 


XIII. 


Milling Machines and Milling 


125 


XIV. 


Gear Cutting , 


135 


XV. 


Precision Grinding .... 


147 


XVI. 


Tapers and Taper Turning 


154 




Tables, Rules, and Notes 


159 






180 



Chapter I 

WORKSHOP ARITHMETIC 

Definition of the Terms used in Arithmetic 

Integer. — A whole number, such as 1, 2, 3, 4. 
Numerator.— The upper number of a fraction is called tne 

numerator ; in the fraction §, 2 is the numerator. 
Denominator.— The lower number of a fraction is the 

denominator; in the fraction |, 8 is the denominator. 
Fraction. — A fraction is part of an integer ; thus 1 divided by 
12 equals the fraction j^. If an inch is divided into 

6-1 parts and 7 of these parts are taken, then the parts 

taken would equal A of the whole, and the fraction 

would be termed a vulgar fraction. 
Proper Fraction.— A proper fraction is one in which the 

numerator is smaller than the denominator, thus 8$. 
Improper Fraction. — An improper fraction is one in which 

the numerator is greater than the denominator ; g$ is 

an improper fraction. 
Mixed Number. — A whole number and a fraction, such as 3$, 

is called a mixed number. 
Factors. — When a number is the product of two or more 

numbers, the numbers used to obtain the product are 

said to be its factors. 
Prime Numbers. — A prime number is one which has no 

factors except itself and 1. Thus 1, 3, 5, 7, 11, etc. 

are prime numbers. 
Multiplicand .— The number to be multiplied is called the 

multiplicand ; thus in 36 x 7, 36 is the multiplicand. 
Multiplier.— The multiplying number is called the multiplier ; 

thus in 36 x 7, 7 is the multiplier. 
Product.— The result of multiplication is called the product ; 

thus 252 is the product of 36 x 7. 
Dividend. — Is the number divided ; thus in 21 •*■ 7, 21 is the 

dividend. 
Divisor. — The number by which another number is divided; 

thus in 21 -f 7, 7 is the divisor. 
Quotient.— The result of dividing; example 21 -j- 7 equals 8, 

then 8 is the quotient. 

B 



2 WORKSHOP ARITHMETIC 

Common Denominator. — The product of all denominators; 

thus the common denominator of J, J, J is 2x3x4 

equals 24. 
Least Common Denominator. — The smallest number all the 

denominators will divide into without a remainder ; the 

least common denominator of }, f, J would he 12, tliat 

being the smallest number 2, 3, and 4 will divide into 

without a remainder. 
Decimal Fraction. — A fraction in which the denominator is 

some power of 10 ; thus ttV, ifor, ttiW ar e decimal 

fractions. 
Sum.— The result of addition; thus 3 + 4 + 5 equals the 

Bum of 12. 
Ratio.— The ratio between two numbers is the quotient 

obtained by dividing the first number by the second ; 

for example, the ratio between 3 and 12 is J, and the 

ratio between 12 and 3 is 4. 
Reciprocal. — Is inverse ratio ; thus the inverse ratio of 3 and 

12 is 12 and 3. 
Proportion. — Is the equality of ratios ; thus 4:2 = 8:4, 

or 4 : 2 : : 8 : 4. 
Percentage. — A ratio in which the denominator is 100. 

expressed by the symbol % . 



Arithmetical Signs and Common Abbreviation* 



+ 


Plus or addition. 


: 


Is to. 


- 


Minus or subtrac- 


: : 


Equals (in pro- 




tion. 




portion). 


± 


Plus or minus. 


V 


Square root. 


=F 


Minus or plus. 


s 
V 


Cube root. 


-r 


Division. 


sin. 


Sine. 


X 


Multiplication. 


cos. 


Cosine. 


log. 


Logarithm. 


tan. 


Tangent. 


■K 


Pi (31416). 


M.E.P. 


Mean effective 


B.H.P. 


Brake horse-power. 




pressure. 


II.P. 


Ilorse-power. 


R.P.M. 


lie volutions per 


I.H.P. 


Indicated horse- 




minute. 




power. 


a 2 


a squared. 


K.W. 


Kilowatt. 


d* 


Diameter squared 





Degree. 


i 


Feet. 


G" 


Square inch. 


•i 


Inches. 


Dia. 


Diameter. 


L.C.M. 


Least common 


.". 


Therefore. 




multiple. 



WORKSHOP ARITHMETIC 3 

Fractions 

The unit of measurement in the United Kingdom is the 
Standard Imperial Yard; this length is divided into three 
equal parts, and eacli part is oalled a foot. A foot, then, is 
a fraction of a yard, and can be stated as one-third (J) of 
a yard. If two feet were tiiken in.sl.pad of one, then the 
distance would be two-thirds (ij) of a yard. 

The foot is divided into twelve equal parts called inches, 
therefore one inch is obviously ^ of a foot. Two inches 
A m f of a foot. Three inches jHj or \ of a foot. Four 
inches ^ or J of a foot, and so on. 

The inch has no special subdivisions, and in workshop 
practice it is divided into any number of divisions to suit the 
particular work on which it is to be used. If it is equally 
divided into sixty-four parts, then one part must be one 
sixty-fourth (g^) of an inch. Two parts fe or fa. Three 
parts £f, and so on. . 

Addition of Fractions 

If an inch is divided into eight parts, each part must be 
k of an inch, and should it be necessary to add together, say, 
i, |, |, and |, it is only necessary to add together all the 
numerators, thus 1 + 3 + 5 + 7 = 16, or ^, which equals 
two whole numbers. The reason for this is that all the 
denominators are of the same power. When it is required 
to add together two fractions with different denominators such 
aa i + ii then it is necessary to find a common denominator. 
The common denominator is found by multiplying the 
denominators together ; thus the common denominator of 
6 and 8 is 48, but as a smaller number can be found which 
can be divided equally by 6 and 8, it is usual to find the least 
common denominatcr, which in this case would be 24. 

If the numerator and denominator of a fraction are both 
multiplied by the same number, then the value of the fraction 
is unaltered, thus : 

J is of exactly the same value a3 A. ° r ifVi or 3%, etc. 

Improper Fractions 

An improper fraction is a fraction in which tho numerator 

is greater than the denominator, thus }g is an improper 

fraction. To bring an improper fraction to a proper fraction 

lue numerator must he divided by the denominator, thus : 

17 + 16 - 1A. 



4 WORKSHOP ARITHMETIC 

Common Denominator 

In order to add together, say, J, J, and $, it is necessary to 
find a common denominator, and this is found by multiplying 
all the denominators together, thus 3 X 4 x 5 = 60 ; then taking 
the first fraction and dividing 60 by 3, we get 20, taking the 
second we get 15, and the third 12. This would be pot 
down thus : 

I + 1 + I 

20 + 15 + 12 _47 
60 " 60 

When the numerators of the fractions to be added are 
greater than 1, then the common denominator is first 
divided by the denominator of the fraction, and the quotient 
multiplied by the numerator, thus jj+S + $ ; here the common 
denominator is 60, and taking the first fraction jj, we divide 
by 3 and multiply by 2, thus 60 -j- 3 = 20, and 20 X 2 = 40, 
giving $fl ; the sum would be put down thus: 

| + f + f 

40 + 45 + 48 188 18 

60 = 60 " 60 



Least Common Denominator 

The leant sommon denominator of any numbers can be 
found by first striking out any numbers which are contained 
ia all the other numbers, and then dividing any of the 
remaining numbers which have a common divisor. Multiply 
all the remaining numbers together, and by the numbers used 
as divisors. 

Example. — Find the least common multiple of 2, 4, 8, 12, 
and 24. Here both 2 and 4 are contained in all numbers, so 
can be crossed out, leaving 8, 12, and 24 ; 4 can be divided 
into numbers 8, 12, and 24, and then 2 will divide into 2 and 
6, and 3 will cancel into 3 and 8, leaving only the three 
divisors 4, 2, And 3, which multiplied together give 24, thui ; 



4 


2, i, 8. 


12, 


•24 


2 


2 


3 


6 


1 


1 


3 


3 




1 


1 


1 



WORKSHOP ARITHMETIC 



Example.— Find the L.C.M. of 12, 16, 28, 42. 



9 


12 16 


28 


42 


•2 


6 8 


14 


21 


3 


3 4 


7 


21 


7 


1 4 


7 


7 




1 4 


1 


1 


n 


s 2 x 2 x 3 


x 7 x 


4 = 336. 



Addition of Vulgar Fractions 
Example. — Find the value of 7 - + § + x l & + :rV 
t + i + A + A 
80 + 70 + 56 + 35 _ 241 
560 560 

Example.— Find the value of 1 J + 1 £ + 2f + 3&. Here the 
Integers are added separately, thus 1 + 1 + 2 + 3 = 7, and then 
the fractions. 

i+$+i+& 



16+40+ 36+15 
48 



48 " l 48 



Which, with the whole numbers, equal 9JJ. 



Subtraction of Fractions 

Proceed in exactly the same manner as for addition, and 
then find the difference in the numerators. 
Example. — J - \. 

a — ? 
7-3 4 



Example. — 1A - A 





21 


21 




J- 

H 


-A 






17-5 
16 


12 _ 

16 


a 
i 



Example. — (J + }) - (J + $). Proceed as for addition, and 
take the fractions in brackets separately. 

(i + *)-(i + i) 

( 42 + 18) - (21 + 14 ) _ 60-35 25 
126 126 126 



B 



WORKSHOP ARITHMETIC 



Multiplicatimi of Fractions 

To multiply fractions, multiply :ill the numerators to obtain 
a new numerator, and then all the denominators to obtain 
a new denominator. 

Example.— Multiply ft by g ; then 7 x 5 = 35, and 16x6 = 96, 
result §§. 

In multiplication the word " ol " ia frequently used in 
place of the word multiply, or the sign x ; thua J of J means 
\ multiplied by £, or J x 1, and which equals ft. 

Cancelling 

Multiplication of fractions is often very much simplified 
by cancelling, thus Jx 5; here it is possible to cancel by 
3 and 2, thus: 

.8 Z_i 

* a~6 

2 3 

Without cancelling we should have ft. Every advantage 
should be taken to cancel when possible. 
Example. — ft x $ x § x jj| x &. Then 

* 3 

B I 1 32 'A _Z_ 

I V, * Z * H * 64 * U " 64 
i 8 

By cancelling in this sum no multiplication is necessary. 

When adding or subtracting whole number* und fractions, 
the whole numbers are in most cases added or subtracted 
separately, but. in multiplication the whole numbers and 
fractions must be always brought to improper fractions. 

Example. — Multiply 2| by lj. Converting these into 
improper fractions we get *£ and %, then 



* 3 



Division of Fractions 

In division of fractions the divisor is simply inverted and 
the fractions multiplied. 

Example.— Divide lj by | or l£ -=- f ; thin inverting the 
divisor we get jj x $, cancelling by 2 and 3 we get 

2 

8 x * -2 



WORKSHOP ARITHMETIC 

Example.— Divide 111 by 2 J, then 
9 

2 

21 

Division is often represented thus rj ; proceed as before : 

1*1 = ,, 

2 

Example.— Divide 301 by If, then 
43 



Decimal Fractions 

A decimal fraction is a fraction in which the denominator 
is 10 or some power of 10. A power of 10 means 10 multiplied 
by itself any number of times, such as 10 x 10 = 100, 
10 x 10 x 10 = 1000, and so on. 

When we write a whole number such as 6666 we indicate 
the number six thousand six hundred and sixty-six. From 
right to left we have units, tens, hundreds, thousands. It is 
quite as easy to start from units and go to the right, 
adding more sixes and calling the digits tenths, hundredths, 
thousandths, etc., thus giving the figures the values ft, T g , 
iifWi etc - ; by doing this with our original figure we can get 
66(56666. To distinguish between the whole numbers and 
the fractions we put a dot called a decimal point, thus 6660-666, 
and the number would then read six thousand six hundred and 
sixty-six whole numbers, and six tenths, six hundndths. and 
six thousandths, or six hundred and sixty-six thousandths. 

Example. — 17-36 means 17 whole numbers and a fraction 
•36, which is ft + i8<j or ftfc. 

To bring a Decimal Fraction to a Vulgar Fraction 

In every case of converting a simple decimal to a vulgar 
fraction, the denominator is a 1 followed by as many 0's ai 
figures in the fraction. 

Examples. -5= ft =i- 1-75 - lfth =1?. 
•25= ft> ff =i. 1-625 = lft$, =1|. 

■l«S-tfJ&-§. i-0625 = irf85 o =iA- 



8 



WORKSHOP ARITHMETIC 



Reduction of Vulgar Fractions to Decimal Fractiont 
To convert a vulgar fraction into a decimal fraction, divide 
the numerator by the denominator, adding noughts as required, 
the decimal point being added to the quotient when the first 
nought is added to the numerator. 

Example. — Convert J into a decimal fraction. To divide 
2 into 1 it is necessary to add a nought, therefore the decimal 
point must be placed in front of the first figure in the 
quotient, thus: 

2)10(-6 
10 



Example.— Convert & into a decimal ; then 16 into 1 will 
not go, so we add a nought and place the decimal point ; 
16 into 10 will not go, so we put a nought into the quotient, 
16 into 100 goes 6 and 4 over, borrowing another nought 
16 into 40 gi-es 2 and 8 over, borrow another nought, 16 into 
80 goes 5, without a remainder. 

This would be put down thus : 

16)10000(-0625 
96 



40 






32 






80 






80 









Answer 


•0625. 


Example.— Convert § into 


a decimal, then 


8)1000(-125 




8 






20 






16 






40 






40 









Answer 


125. 



WORKSHOP ARITHMETIC 

Example. — Convert fa into a decimal, then 

64) 1000000(- 015625 
64 



400 
884 

160 
128 



320 
820 



Answer -015625. 



Examples. J «= 1 + 4 = 0-25. 

t = 8-i- 8 = 0-375. 

8* = 7* 8 = 0-875. 

A = 8-5- 16 = 0-1875. 
f|*10* 16 = 0-9375. 

& = 1 * 32 = 0-03125. 

ft- 3 -r 64 = 0-046875. 



Repeating Decimals 
When a fraction such as J is converted into a decimal 
fraction, it will be found that the figure in the quotient simply 
repeats, thus 1 -^ 3 = -333; this is called a recurring or 
repeating decimal. In the case of | being converted into 
a decimal fraction it will be found that a certain set of figures 
recurs, thus 1 -f 7 = -142857 ; these figures go on recurring 
indefinitely, and it is called a circulating decimal. In the 
case of a fraction like $§ wc get 21 + 22 = -95454, with the 
figures 54 only repeating ; this is called a mixed circulating 
decimal. 

In the first case the decimal is expressed as -3, the point 
above the figure indicating that the figure repeats. In the 
second case the decimal would be indicated as -142857, 
showing that all figures recur. In the last example, as -954.' 
•bowing that the figures 54 only repeat. 



10 



WORKSHOP ARITHMETIC 



To bring Repeating Decimals to Vulgar Fractions 

Pure recurring decimals such as -8 and «54 can bo brought 
to vulgar fractions by making the recurring figures the 
numerator and placing a 9 or as many 9's as there are figures 
as the denominator, thus : 

•a = | or A. -64 = fa. 



Fractions and Decimal Equivalents 


«r* 


015625 


81 


•515625 


sS 


03125 


y 


•53125 


ft 


046875 


n 


•546875 


A 


0625 


& 


•5625 


ft 


078125 


u 


•578125 


& 


09375 


H 


•59375 


ft 


109375 


it 


•609375 


j 


125 


a 


•625 


ft 


140625 


ft 


•640625 


A 


15625 


R 


•65625 


8 


171875 


I 


•671875 


A 


1875 


1 


•6875 


H 


203125 


i 


•703125 


A 


21875 


i 


•71875 


8 


234375 


I 


•734375 


i 


25 


s 


•75 


8 


265625 


if 


•765625 


s 


28125 


1 


•78125 


8 


296875 


H 


•796875 


A 


3125 


H 


•8125 


8 


328125 


u 


•828125 


H 


34375 


n 


•84375 


y 


859375 


81 


•859375 


I 


875 


s 


•875 


1 


390625 


81 


•890625 


H 


40625 


H 


•90625 


n 


421875 


81 


•921875 


A 


4375 


H 


•9375 


H 


453125 


Si 


•953125 


y 


46875 


B 


•96875 


» 


484375 


9 


•984375 


j 


5 


i 


10 



WORKSHOP ARITHMETIC 



11 



To bring Mixed Circulating Decimals to Fractions 
To find the numerator subtract the digits which do not 
recur from the whole fraction, thus -2136 = 2136-21--= 2115. 

To find the denominator place a 9 for every figure recurring 
and a for each nou-rccurring figure, thus -213b = $iJ&. 
Example. — 2136 = <jJJS = #& = AV 
Examples. -1236 = ftMft = iVs- 

•081 = $, = xfcp 
•7 = J. 
•0963 = m> = dfV 

Decimals 

Addition 

The rule for the addition of decimals is: The decimal point 
must be placed directly under t.lie preceding one. 
Example.— Add 2-75, 1-0125, 14-7854, then 
2-75 
1-0125 
14-7854 



18-5479 Answer. 

Example.— 1-03 +-125 + -0002 + 84-5, then 
1. 08 
•125 
•0002 
84-5 



85-6552 Answer. 

Subtraction 

Rule. — The same as for addition. 

Example. — Subtract 1-025 from 6-1416, then 

6- 1416 

1-025 



5-1166 Answer. 



Example.— 3-1854-2-973, then 
8*1864 

2-973 



■2124 Answer. 



12 



WORKSHOP ARITHMETIC 



Multiplication 

Rule.— Tut down the figures as for simple multiplication 
and multiply in the ordinary manner. The number of figures 
to be marked off in the product is the sum of the decimal 
places in the multiplier and the multiplicand. 
Example. — Multiply 27-126 by 19-43, then 
27-126 
19-43 



81378 
108504 
244184 
27126 

627-05818 



We have three places of decimals in the multiplicand and two 
in the multiplier, so we mark off five places in the product. 
Example.— 3-1416 x -015, then 

3-1416 
•015 



157080 
31416 

•0471240 



Here we have four places in the multiplicand and three in the 
multiplier, so we must mark off seven figures in the product; 
as there are only six we add a and place the deoimal point. 



Division 

Rule. — Make the divisor a whole number by removing the 
decimal point. Shift the decimal point in the dividend as 
many places to the right as there were decimal places in the 
divisor, adding ciphers if necessary. Divide as for ordinary 
division. Then place the decimal point in the quotient whoa 
bringing down the first decimal place of the dividend. 
Example. — Divide 11-65 by -008, then 
8 | 11650-00 

1456-25 Answer. 



WORKSHOP ARITHMETIC 

Example,— Divide -0846 by -09, then 
9 |_3 1 460 

-884 Answer. 

Example.— 93-576 -7- 614, then 

614)9357-600(15-2403 
014 

8217 
3U70 

1476 
1228 

2480 
2456 

2400 
1842 



13 



558 Answer 15-2403. 



Example.— 14-1 4- 0037. 



37)141000-00(3810-8108 
111 

800 

396 

40 
87 

800 

296 

40 
87 

800 
896 



4 Answer 3810-810. 



14 



wortKsnop arithmetic 



Recurring and Circulating Decimals 
Rule.— Cany the circulating decimal two places more than 
the required number of accurate decimals. 

Example.-- Subtract 1 - 2<"i from 2-97 to three places of 
decimals, then 2-97777 

1 -20262 



1*71518 Answer 1-715. 



Example— Find the sum of 2-51-i and 1-63 to four places 

of decimals, then _, _,,... 

2-51-1444 

1*686868 



4-150807 Answer 4-1508. 



Example.— Find the product of 2-403 and 1-26 to three 
places of decimals, then 

2-40340 
1-26262 



480680 
1442040 
480680 
14-12040 
480680 
240340 

3 • 0846808080 Answer 3 • 034. 



Example.— Divide 2-403 by l-o to three places of decimals. 

6n : l-66666)2-40340(l-442 

1-66666 

736748 
660664 



700794 
666664 

341300 
833332 



7968 Answer 1-442 



WORKSHOP ARITHMETIC 



J6 



A more accurate and much quicker method of dealing with 
circulating decimals is to bring them to vulgar fractions, and 
then add, multiply, or divide as required. 



Ratio and Proportion 

Ratio is a term indicating the relationship that exists 
between two numbers or two quantities of the same kind, and 
can be ascertained by dividing the first quantity by the second. 
For example, if it is required to cut a screw having 24 threads 
per inch in a lathe having a lead screw of 4 threads per inch, 
tlie ratio would be 24-4-4 = 6, or 6 to 1. 

A ratio is not altered if both of the terms are multiplied or 
divided by the same number. For example, the ratio of 24 
to 4 is the same as 12 to 2 and 6 to 1. 

Ratios can only be expressed between two quantities of the 
lime kind. Thus it is not possible to compare yards with 
inches or pounds with tons. 

Ratios are often conveniently expressed as fractions, 
especially when the first term is smaller than the second. 
Thus the ratio between 2 threads per inch and 4 threads per 
Inch can be expressed as J. 

Proportion 
Proportion is the equality of ratios or the relationship 
between four quantities. Thus, as 8 is to 4 60 ie 10 to 5. The 
first and last terms in a proportion are called the extremes ; 
the second and third are called the means. And the product 
of the extremes is equal to the product of the means. Thus 
8 : 4 : : 10 : 5, then 8x5 = 40 and 4x10 = 40. 
If three terms of a proportion are known, the remaining 
term can be found by the following rules : — 

1. The first term is equal to the product of the second and 
third teems divided by the fourth. 

Example. — Let x be the term to be found, then 
x : 4 : : 5 : 15. 

2. The second term is equal to the product of the first and 
fourth terms divided by the third. 

Example. — lj : x : : 5 : 15. 



16 



WORKSTIOP ARITHMETIC 



8. The third term is equal to the product of the first and 
fourth terms divided by the second. 
Example. — 1$ : 4 : : s 16. 



4 



= 5. 



4. The fourth term is equal to the product of the second 
and third terms divided by the first. 
Example.— 1J : 4 : : 5 : x. 

""TT 



?=1*. 



Percentages 

If 100 gauges are made and 3 are rejected as being under 
size, then it is said that 3 per cent were unsuitable. Per- 
centage, then, is a ratio in which one term is a hundred, and 
the other term expresses the rate per hundred, or is the rate 
per cent. 

Rule 1. — If the percentage is given, multiply the given 
quantity by the percentage and divide by 100. 

Example. — What is 7 per cent of 95 ? Then 

100 
Example. — If 2 per cent of 750 turning jobs are spoilt, how 
many are remaining ? Then 

^=15, 750-15 = 735. 

Rule 2. — If the percentage is required, multiply the part by 
100 and divide by the whole. 
Example. —What percentage of 95 is 6-65 ? Then 
6-65xlQQ _ f><> , 
95 '*' 

Example. — If 15 jobs are spoilt out of 750, what is the 
percentage ? Then 

15 x 100 



750 



= 2%. 



Proportional Parts 

When an alloy is composed of several metals and the total 
weight is given and also the proportion of its component 
parU, the weight or value of each metal can be found. 



WORKSHOP ARITHMETIC 



17 



The number of parts of each metal will be the numerator 
of a fraction of the whole, and the total number of parts of all 
the metals will be the denominator. 

Example. — White metal to the weight of 16 lb. is run into 
a bearing; the composition of the alloy is 25 parts tin, 2 parts 
antimony, and 1 part copper. Then, total number of 
parts 28. 

Weight of tin ■ 



28 



:= 14-29 lb. 



Weight of antimony=^i^ = 1141b. 
28 

Weight of copper = Li!!? = 0-57 lb. 
2o 

Averages 

If 3 jobs are spoilt out of 96 the average number of jobs 
spoilt would be 1 iu 32. Thus the average of any number of 
quantities is the result of dividing the sum of the quantities 
by the number of them. 

The average is also called the mean of the quantities. 

Example. — If a turner finishes 1G jobs on Monday, 15 jobs 
on Tuesday, 17 Wednesday, 13 Thursday, 16 Friday, and 
7 Saturday, the average number per day would be 
(16-rl5 + 17+13 + 16 + 7)-r6 = 14. 

Formulae 

The term formulas may be defined as a rule in which 
symbols or letters are used in the place of words ; in fact» 
h formula is a shorthand method of condensing words or 
sentences into a small space. 

The letters used in formula simply stand in place of figures, 
which are to be substituted when solving a problem. 
Example. — Formulas for finding the area of a circle. 
A = -7854x£f 1 . 
Here A stands for area of the circle and d for the diameter o.' 
the circle in inches. 

Example. — Formulas used in gearing problems. To obtain 
outside diameter, having number of teeth and diametral 
pitch. 

Let D=outside diameter. 
„ N = number of tenth. 
„ P = diametral pitch. 

ThenD = *±l 2 



18 



WORKSHOP ARITHMETIC 



Example. — Number of teeth 22, diametral pitch 12. Find 
outside diameter. Substituting figures for letters, we get 

22 + 2 



D = 



12 



- = 2. 



Example. — To obtain diametral pitch having number of 

teeth and outside diameter. 

N" + 2 
Formula P = -— — 

Example.— Number of teeth 22, outside diameter 2, then 
22 + 2 

When several numbers or quantities in formulas ore 
connected with signs indicating that multiplication, division, 
subtraction, or additions are to be made, generally multiplica- 
tion should take place before any other operation. Division 
also precedes addition and subtraction if written in a line 
with these. The other operations are carried out in the 
order given. 

Example.— Find the value of 42 - (27 + 14) + 7 x (15 - 3). 
Then 42- (27 + 14) + 7 x (16-8) 
= 42-41+ 7x12 
= 42-41 + 84 
= 1 +84 

= 85 Answer. 

Example.— Find the value of (3J + 2J) + 6J. 
Then (3i + 2J) + 5.1 
= 5J + 5i 
= 5jxA = lfl 1 ! l . 

3i + 2J 
Example. — Find the value of g- | _ «i 

Then tj±a 

= (3i + 2}) + (3i-2j) 

Figures shown in parentheses or brackets must always be 
calculated independent of all other figures, and if one bracket 
Is placed inside of another the one inside must be calculated 
first. 



WORKSHOP ARITHMETIC 
Example.— Find the value of 5 - [g + {3J - (2 J - lg)}] 



19 



Then 5 - [ft + 
-5-H+ 

= 5-[| + 
= 5-[g + 

-5-L8 + 8A] 
= 5-4* 

= !• 



sj-(2i-ij)H 
32 -(il)}] 

3 A}] 



Simplified Method* of Arithmetic 

To multiply by 10, add a nought, or shift the deoimal point 
to the right one place. 

Example.— 7 x 10 = 70. 

187'561 x 10 = 1875*61. 

To divide by 10, cross off the last figure, or shift the 
decimal point to the left one place. 

Example. — 170 + 10 = 17. 

187-561 + 10 = 18-7561. 

To multiply by 25, add two noughts, and divide by 4 ; if 
decimals, move decimal point to the right two places, and 
divide by 4. 

Example.— 27 x 100 = 9700 

= 9700 + 4 = 2425. 
97-65 x 100 = 9765. 
= 9765 + 4 = 2441-25. 

To divide by 25, cross off last two figures, or shift decimal 
point two places to the left, and multiply by 4. 

Example.— 9700 -=- 25 = 

97 x 4 = 388. 

To multiply by 5, add a nought, or remove the decimal 
point one place to the right, and then divide by 2. 
Example. — 72 - 6 x 5 = 

726 + 2 = 863. 

To divide by 5, strike off last figure, or move the deoimal 
point one place to the left, and multiply by 2. 

Example.— 7 "26 + 6 = 

•726x8-1-462. 



20 



WORKSHOP ARITHMETIC 



To multiply by 9, add one cipher, or move the decimal 
point one place to the right, and subtract the original number. 
Example.— 7624 x 9 = 

702 10 -7624 = 68616. 

To multiply by 101, add two ciphers, and then add the 
original number. 

Example.— -5217 x 101 = 

521700 + 5217 = 526917. 

To multiply by 125, add three ciphers, and divide by 8. 

Example.— -27 '4 x 125 - 

274000 + 8 = 34250. 

To divide by 125, strike off last three figures, and multiply 
by 8. 

Example. — 875000 + 125 = 
875 x 8 - 7000. 



Tables 

Long Measure 

English 

12 (") inches = 1 (') foot. 

3 feet = 1 yard (yd.). 

5J yards = 1 pole. 
40 poleB = 1 furlong. 

8 furlongs = 1 mile. 

Metric 
10 (mm.) millimetres = 1 centimetre. 
10 (cm.) centimetres = 1 decimetre. 
10 (dm.) decimetres = 1 metre. 
10 (in.) metres = 1 decametre. 

10 Dm.) decametres = 1 hectometre. 
10 (Hm.) hectometres = 1 kilometre (km.). 

English Equivalents of Metric Measures of Length 

1 millimetre = 0'03937 inch or about ^ of an inch. 

1 centimetre =0'3937inch. 

1 decimetre = 3937 inches. 

1 metre = 393707 inches. 

1 decametre = 32 8089 feet. 

1 hectometre = 19 '927 poles. 

1 kilometre = 109361 yards or 06213 of a mil*. 



WORKSHOP ARITHMETIC 



21 



Squ/J7-e Measure Cubic Measure 

144 sq. in. =1 sq. ft. 1728 cubic inches = 1 cubic foot. 
9 sq. ft. = 1 sq. yd. 27 cubic feet = 1 cubic yard. 

30£ sq. yds. = 1 sq. pole. Angular Measure 

40 sq. poles = 1 rood. 60 (") seconds = 1 (') minute. 
4 roods = 1 acre. 60 minutes = 1 (°) degree. 
640 acres = 1 sq. mile. 90 degrees = 1 right angle. 

4 right angles = 1 complete 

circle. 

Avoirdupois Weight 



16 drams = 
16 ounces 

14 pounds = 

28 pounds = 

4 qrs. or 112 lb. ■= 

20 hundredweights = 



1 ounce (oz.). 

1 pound (lb.) 

1 stone. 

1 <|iiarter (qr.). 

1 hundredweight (cwt.). 

1 ton. 



CHAPTER II 
MENSURATION AND GEOMETRY 

Mensuration 

Area of Surfaces 



Fro. 1. — Square. Let ft equal length 
of any side, then 



* 3 » 




a > 



area = ft 8 



Fr«. 2. — Rfwmbus. Area 
equals length of base, multiplied 
by the perpendicular height, 
then 

area = a x b. 



Fio. .'5. — Trapezoid. Area 
equals half the sum of the two 
parallel sides, multiplied by the 
perpendicular distance between, 
then 

a + b 

urea = x c. 



i Fig. 4. — Rectangle or Oblong. 

b Area equals length, multiplied by 

• breadth, then 
i 

' area = a x b. 



<- . . . a 1 



MENSURATION AND GEOMETRY 



Fir.s. 5 and 6. — Tri- 
angles. Area of a tri- 
angle, such as Figs. 5 
and 6, equals length of 
buse, multiplied by one- 
half of the perpendicular 
height, then 

area = a x J b. 



23 




«... a 



Fig. 7. — Circle. — Area equals diameter 
squared, multiplied by -7854, then 
area = d 2 -7854. 



Fig. 8. — Circle. Area equals radi 
squared, multiplied by 3-1416, then 
area = ?" *\ 



Fig. 9.— Sector of a Circle. Let 
b equal length of arc of circle, and »»^ 
r radius of circle, then 

area = b x 

Ss 

Fig. 10. — Segment of a Circle. 
Let /) equal length of chord and ft 
height of segment, then approx. 
a x 2 x b ft 3 

+ • •- b 



area = 



2 x 



Fig. 11. — Segvient of a Circle. 
Let r equal radius of circle, 
b length of arc of segment, and 
I breadth of base of segment, 
then 

—(«-t) -(»-!)■ 






24 




MENSURATION AND GEOMETRY 

Vic. 12. Ellipse, Let a equal maxi- 
mum length, 6 maximum breadth, then 

area = 0*7864 x ax b; or, 
let a and b equal half maximum length 
and breadth, then 

area = a x b x *. 



Fig. 13. — Hemisphere. Area of 
hemisphere equals half the area of a 
sphere of equal diameter. 



Fig. 14.— Sfhere. Let d equal diameter 
of sphere, then 

area — ird*. 



<--■ d-~> 




(■--a --.> 



Fig. 15.— Cube. Let a 
length of any side, then 
area = (in ". 



equal 




Fig. 16.— Cylinder. Let 

/ equal length of cylinder, 
and d diameter, then total 

area = M x I) +%(jd 2 ). 



i > 



MENSURATION AND GEOMETRY 



25 



I'lii. 17. — Cone. Area equals circum- 
ference of base, multiplied by one-half 
slant height, plus area of base ; or, 

Let a-b equal slant height, a-c dia- 
meter, a-d radius of base, then 

ir x ab . , , ,o . 

+ (dc)* x ■*, 



total area = 




Fig. 18. — Frustum of a Cone. Area 
of the moved surface equals half the sum 
of the two ends, multiplied by w and 
multiplied by slant height. 

Let a, 6, c, d equal frustum, a-b = 

slant height, a-d and b-c = the two 

diameters, then 

ad + be , 

area = — x w x ab. 




Fig. 19. — Pyramid. Area equals peri- 
meter of base, multiplied by half slant height, 
plus area of base. 




Fig. 20. — Hexagon. Let I equal length 
of one side, w width across flats, then 
area = 2-598 x I* or area = 0-866 x «j a . 



*--/ --♦ 



Fig. 21. — Polygon. Let r equal radius of 
inscribed circle, I length of one side, n number 
of sides, then 

area = Jr x I x n. 



•'I'* 



26 



MENSURATION AND GEOMETRY 



MENSURATION AND GEOMETRY 



27 



Volumes of Solids 

Volume of a Cube — 

Let v = volume. 

I = length of aide. 
Then v = I 3 , or 
1= Vv. 

Volume of a Square Prism — 

Let v = volume. 
I = length. 

6 = breadth, and width. 
Thent>= lb 1 . 



■-*.»- Vf 



Volume of a Sphere — 

Let v = volume. 
d = diameter. 

Then v = ~ x d*. 

Volume of a Cone — 

Let v = volume. 

d = diameter of base. 
h = slant height. 

Then v = -^- x d* x h. 
12 

Volume of a Cylinder — 

Let v = volume. 
d = diameter. 
I = length. 
Then v «= 0-7854 x d fl x I. 

Volume of a Pyramid — 

Let v = volume. 

a «= area of bate. 
h «» height. 
Then v ■ $ h x a. 

Volume of a Frustum of a Pyramid — 
Let v = volume. 
d ~ area of base. 
a* m area of top. 
h m height. 

Then v - — (a, + a% + ^aTx~a^ 

a 



Geometry 

Fig. 22. — To divide a line into two 
equal parts. Let a- b represent the line 
to be bisected, then with a and 6 as 
centres and with a radius greater than 
one-half the length of the line draw arcs 
as shown. Through the intersections of 
the arcs draw a line. This line divides 
a-b into two equal parts and is per- 
pendicular to the horizontal line. 



Fir.. 23.— To divide an angle 
into two equal parts. Let b, a, c 
equal the angle, then with a as 
centre and any radius draw arcs at 
d and e. With d and e as centres, 
and a radius greater than one-half 
the angle, draw arcs at /. A line 
drawn through the intersections at 
f to a divides the angle into two 
equal parts. 



FIG. 24. — To draw a line perpendicular 
to a straight line from a given point. 
Let c be the point. Then with c as 
centre and any radius draw arcs at a and 
h, with a and 6 as centres and radius 
greater than a c, draw intersecting arcs 
at d. Line d-c is then perpendicular 
to a-b. 



Fir.. 25. — To divide a line into two 
rni/al parts. Let a-b represent the 
line. Then with a and b as centres 
and any radius greater than half the 
length of the line, draw circular arcs. 
A line drawn through the inter- 
sections at d and c divides a-b into 
equal parts. 



* 



I 




28 



MENSURATION AND GEOMETRY 







c d 

the radius. A line just touching the arcs is parallel to a-b. 



Fig. 26. — To divide a straight 
line into any number of equal 
parts. Let a-b represent the 
line and the number of parts 7. 
Draw the line a-c at an angle 
to a-b. Mark off on a-c seven 
equal divisions of any con- 
venient length. From mark 7 
draw a line to b, and then draw 
lines parallel to 6-7 through 
6, 5, 4, 3, 2, and 1. 

Fig. 27. — To draw a line 
parallel to a given line at 
a given distance. Let a-b 
represent the line. From 
any points, c-d, draw arcs 
with the given distance as 







><f 



Fig. 28.— To draw a 45° angle. 
Let a-b represent the line. Then 
from a, set off any distance a-c. 
Draw the perpendicular c d, and with 
a distance equal to c-a mark off d. 
Draw line from d to a. Then c, a, d 
equals angle. 



FlG. 29. — To draw a per- 
pendicular to a line from a 
point. Let 6-c represent the 
line and a the point. Then 
with a as centre draw an 
arc cutting the line at d-e, 
with d und e as centres, draw 
arcs with radius greater than 
one-half the distance between 
d and e. If the arcs intersect 
at a and/, then a line drawn 
through the intersections will 
betherequired perpendicular. 






MENSURATION AND GEOMETRY 29 



Fig. 30. — To draw a per pendicnl 'in- 
line from a point at the end of a. line. 
Let a-b represent the line and a the 
point. Take any centre c, and willi 
radius c-a, draw an arc cutting a-b at 
d. From d draw a line through c lo e, 
and then join a-e. This line is the 
required perpendicular. 

Fig. 31. — To draw an angle of 60°. 
With a as centre and any radius, draw 
arc c-b. With b as centre and b-a as 
radius, draw an arc intersecting the 
arc just drawn at c. Draw a line 
from c to a. Then 6, a, c is the 
required angle. 



Fig. 32. — To draw an angle of 30". 
Mark off as for an angle of 60°, then 
bisect arc c-b. 



Fig. 33. — To repro- 
duce a given angle. Let 
a, d, c represent angle 
to be reproduced. Then 
with a as centre draw 
arc d~c of any radius. 
With e as centre draw f-g with the same radius. Make h-g 
equal c-d, and draw k-e through h. Angle e, k, g will 
equal a, c, d. 



Fig. 34.— To find Oie centre 
of the arc of Oie segment of a 
circle. From points a and b, 
with length a-b, draw arcs at c. 
The point of intersection will 
be the centre of the arc. 





* 






90 MENSURATION AND GEOMETRY 



Fig. 35. — To inscribe a hexagon in 
a circle. Draw diameter a-b with c 
as the centre, with radius a-c mark 
off points intersecting at d, e, b. g,f. 
Then join a-d, de, e b, by, gf, and 
a/to form the hexagon. 



Fig. 36. — To describe a hexagon 
about a circle. Draw diameter 
from b, with a-b as radius cut the 
circle at c. Join a-c and bisect 
with a line drawn from b. Where 
this line touches the circle draw a 
line e-f parallel to a-c. Willi 
b as centre and b c as radius draw 
a circle. Within this circle describe 
the hexagon. 

FlG. 37. — Draw a regular polygon 
when one side is given. Let a-b 
represent the given side. With a as 
centre, and a-b radius, draw the semi- 
circle c, e, b. Divide the semicircle 
into as many equal parts as the polygon 
has sides. This is done by trial. Join 
the second point of the division e to a : 
this is the second side of the polygon. 
From the centre of sides ea and ab, 
draw perpendiculars which will intersect at /. With / as 
centre, and radius fa, draw the circle containing the polygon, 
and with radius a e mark off the sides. 

FlG. 38. — To find the centre 
of an arc of a circle. Mark 
off three points on the peri- 
phery of the arc a, b, c, and 
with each of these points as 
a centre and the same radius 
describe arcs intersecting each 
other. Through the points 
of intersection draw the lines 
c d and ef. The point where 
these lines intersect is the 
centre of the circle. 



MF.NsntATION AND GEOMETRY 



81 





Fiu. 39.— To describe a circle 
about a triangle. Divide the 
sides a b and ac into equal parts, 
and from the division points de 
draw lines at right angles. The * 
point of intersection is the centre 
of the circle. 




Fig. 40. — To inscribe a circle 
in a triangle. Bisect two of the 
angles a and b, and the point of 
intersection is the centre of the 
circle. 




Fig. 41. — To describe a square 
about a circle. Draw line b-c 
through centre a of circle. Draw 6 
lines parallel to 6 c at d and e, and 
also lines at right angles at c and b. 






32 



MENSURATION AND GEOMETRY 



MENSURATION AND GEOMETRY 



83 










2 


34 56 7 


yS^^ 


r > 




s 










/ 








\ 








1 


\ 








\ 






r 


J 










\ 




\ 












\ 


^ 


\~^_ 


^ — 








- 




^r 



Fig. 42. — To construct an 
involute. Draw base circle 
a-b and divide into any 
number of equal parts. 
Through the division points 
1, 2, 3, 4, etc., draw tan- 
gents to the circle and make 
the lengths c, d, e, f, etc. , 
of these tangents equal the 
length of the arcs al, a2, 
a'6, al, etc. 



Fig. 43. — To construct 
a helix. Divide half the 
circumference of the cylin- 
der on which the helix is 
to be described into a 
number of equal parts. 
Divide half the lead of the 
helix into the same num- 
ber of equal parts. From 



the division points on the circle representing the cylinder 
draw horizontal lines, and from the division points on the lead 
draw vertical lines as shown. The intersection between lines 
numbered alike are points of the helix. 



Distance across Corners of Squares and Hexagons, given 
distance across fiats 

Flats of hexagon x 1-155 equal distance aoross corners. 
,, square x 1-414 ,, ,, ,, ,, 



Across 


/~\ 


/\ 


y\ 


Flats. 


\J 


\J 


X> 


1 


•29 


•33 


•36 


A 


•36 


•41 


•44 


i 


•43 


•50 


•53 


a 


•50 


•58 


•62 


k 


•67 


•66 


•71 


A 


•65 


•75 


•80 


| 


•72 


•83 


•88 


H 


•79 


•91 


•97 


J 


•86 


100 


1-06 


H 


•93 


1-08 


115 


i 


101 


116 


1-24 


U 


1-08 


1-25 


1-83 


l 


115 


1-88 


1-41 


iA 


1-22 


1-42 


1-50 


11 


1-29 


1-50 


1-59 


ift 


1-37 


1-58 


1-68 


i* 


1-44 


1-66 


1-77 


iA 


1-61 


1-75 


1-86 


is 


1-5& 


183 


1-94 


iA 


1-66 


1-92 


2-03 


14 


1-73 


2-01) 


212 


IA 


1-80 


208 


2 21 


H 


1-88 


216 


2-80 


m 


1-95 


2-25 


2-89 


i* 


202 


2-83 


2-47 


i? 


209 


2-42 


2-50 


2-17 


2-50 


2-65 


itf 


2-24 


2-58 


2-74 


i 


2-31 


2-66 


2-83 



Chapter III 

MATERIALS 

Iron 

It has been estimated that the earth's crust is composed 
of about 4J to 5 per cent of iron. In many places stone 
containing up to 73 percent of iron is found ; seldom is the latter 
found in the free state, and therefore it requires to be smelted. 
Iron-ores are invariably found mixed with earthy matter, 
making them refractory, and requiring the addition of a flux 
to combine with the earthy matter and facilitate fusion. 

The chief iron-ores are : — 



Namk ok Our.. 



Red hematite. 

Magnetic ore. 
Spathic iron-ore. 
Brown hematite. 
Clay ironstone. 



Cuemical 
Composition. 



% 

OF 

Ore, 



Wheue foond. 



Anhydrous 
ferric oxide. 

Black oxide 
of iron. 

Perrons car- 
bonate. 

Hydrated 
ferric oxide. 

FerrouB car- 
bonate. 



60 Spain, Furness District. 

United States, G-ermany, 

Canada. 
02 Norway, Sweden. 

35 Durham, Yorkshire, Derby. 

Somerset, Wales, Scotland. 
42 Lincolnshire, Forest of Dean, 

Spain, France, Germany. 
33 England, Wales. Scotland. 

Germany, Russia, Hungary. 



Iron is used in general engineering work in three varieties, 
cast iron, wrought iron, and steel, the difference being in 
the amount and the form of the carbon they each contain. 
The methods of obtaining these metals are : — 

Pig Iron. The product of tbe blast furnace, obtained from 

iron-ore, by smelting with the aid of fluxes. 
Cast Iron. Iron obtained by melting pig iron in the 

foundry cupola, and used for running into moulds 

for making iron castings. 
Wrought Iron. Pig iron, refined, and then puddled in the 

puddling furnace, afterwards hammered and rolled into 

bars, plates, etc. 



MATERIALS 



36 



Steel. Compound of iron and carbon, obtained by first 
abstracting the whole of the carbon, and then adding 
more carbon to combine with the iron. Manufactured 
by the Siemens process, the Bessemer process, the 
Cementation process, tbe Basic process, and by 
crucible. 

The Blast Furnace. — The blast furnace is usually con- 
structed of wrought iron or steel plates, lined with fire-brick 
or some other refractory material. It takes the form of two 
truncated cones joined at their bases, with a short parallel 
part at the bottom forming the hearth ; the whole being 
usually built on a foundation of sandstone, and supported by 
cast-iron pillars. 

The size of the furnaces varies between 50 and 100 feet in 
height, the largest size producing as much as 3,000 tons of 
pig iron per week. 

In order to produce 1 ton of pig iron it is necessary to use 
about 40cwt. of iron-ore, 20cwt. of coke, and 8cwt. of lime- 
stone. 

The charge, which consists of definite quantities of ore, 
coke, and limestone, is taken to the top of the furnace either 
by means of an hydraulic lift or else on an inclined hoist. 
It is then dropped into the hopper receiver, the ball of which 
is lowered to admit the charge into the furnace. Charging 
takes place about once every fifteen minutes, and forms 
a layer all round the furnace, keeping the mass at a constant 
level. The ball and hopper arrangement at the top of the 
furnace prevents the escape of hot gases during the charging 
process. 

As the furnace is widest and largest in the centre and 
tapers downwards, it thereby prevents any large mass of 
metal falling on the hearth. The iron being heavier than 
the fuel gradually sinks, gaining more heat as it proceeds 
downwards, and at the same lime becoming more liquid. As 
the molten mass falls it carries with it cinders and slag, 
which rise to the top and are allowed to pass off through an 
opening about 3 feet above the floor of the hearth, into cinder 
tubs. The amount of slag obtained is about equal to the 
amount of pig iron produced. To aid combustion, air pre- 
viously heated to a temperature of about 1,200° Fahr. is blown 
in by means of a special blowing engine ; the pressure of tbe 
air depends upon the height of the furnace, and varies 
between 3 and 121b. per square inch. The blast is admitted 
to the furnace through special water jacketed tuyeres. 



36 



MATERIALS 



The waste gases given off by the furnace, which are the 
product of the combustion of the fuel, are utilized for heating 
the air blast, working the blowing engine, and in some cases 
liring the boilers of the works. 

When the hearth of the furnace is fully charged with 
molten metal, it is tapped, about eight hours being required to 
provide the full amount. The tapping simply consists of 
knocking in a plug of fire-clay, which allows the metal to run 
out into the sand channel ready to receive it. The main 
channel leads to a smaller channel called a sow, from which 
smaller channels lead into sand moulds, the latter being 
termed pigs. The pigs are about 8 feet long and 4 inches wide. 

When pig iron is intended for conversion into steel, it is 
not run into pigs, but direct into ladles ready for transportation 
to the metal mixer, whence it goes direct to the converters 
or steel furnaces. 

Pig iron contains from 3 to 4'5 per cent of carbon, about 
3 per cent being in the form of graphite or blacklead, the 
remainder being chemically combined with the iron. 

Tlie Cupola. — The foundry cupola consists of a vertical 
cylindrical vessel constructed of steel plates and lined with 
fire-In iek, a door near the top being provided for introducing 
the charge ; at the bottom is the hearth upon which the 
molten liquid collects. In order to produce the necessary 
heat to melt the iron, air is blown into the mass of coke and 
iron through tuyeres placed at the bottom of the furnace. 

The charge is made up of layers of broken pig iron, coke, 
and limestone, the usual amount of coke and limestone being 
about 2h cwt. of coke and J cwt. of limestone to 1 ton of pig 
iron. The molten metal is tapped into a ladle and run into 
moulds as required. 

The pig iron used for foundry purposes is termed grey iron, 
and is classified Nos. 1, 2, 3, and 4 (foundry) ; the amount 
of combined carbon increasing as the numbers rise, and the 
amount of silica decreasing. 

Tlie Puddling Furnace. — In order to produce wrought iron 
of good quality, pig iron from the blast furnace iB first put 
through a refining process, the object of which is to convert 
or abstract the whole of the uncombined graphite. This 
object is accomplished by melting the metal, and forcing 
a blast of air on to the surface of the molten metal, and 
thereby oxidizing the carbon and producing what is known as 
white iron. 

The puddling furnace is made up of cast-iron plates lined 
with fire-brick, with a dome-shaped roof to reflect the heat. 



MATERIALS 



87 



The hearth of the furnace is lined with oxide of iron or tap 
cinder, and the charge consists of about 4 cwt. of white iron ; 
this amount requires about half an hour to become partly 
melted, and to form a pasty mass. When it is in this state 
it is thorougly rabbled with the tap cinder, in order to bring 
every part under the oxidizing influence of the oxide of iron ; 
the carbon then combines with the oxygen and passes off 
as C 2 . 

At this stage of the process jets of flames known as 
puddler's candles are formed, the slag begins to drop, and 
particles of malleable iron float on the surface, forming 
a spongy mass. These particles are worked together by the 
puddler and made into balls. The balls are taken to the 
shingling hammer and then hammered, so that the slag is 
squeezed out, and the iron welded together, forming what is 
known as blooms. To improve the quality of the iron, the 
blooms are reheated, piled four high, and welded into 
billets, and (hen again reheated and rolled into bars, plates, 
angles, etc. 

Steel 

Steel is a compound of iron and carbon, or iron, carbon, and 
some other element, forming an alloy or compound capable of 
being hardened by a sudden cooling. Carbon steels of the 
mild steel quality contain not more than 0'2 per cent of 
carbon, medium steels up to 05 per cent, hard or high carbon 
steels up to 1 '6 per cent. 

Alloy Steels — Steels which owe their properties chiefly to 
the presence of an element other than carbon are called alloy 
steels. 

Bessemer Steel. — Steel made by the Bessemer process. 

Blister Steel. — Steel made liy the Cementation process. 

Crucible Steel. — Steel made by the Crucible process, 
irrespective of the carbon content. 

Open Hearth Steel. — Steel made by the Open Hearth 
process, irrespective of the carbon content. 

Shear Steel. — Steel usually made from blister steel by 
cutting bars into short lengths, then piling and welding 
them, by hammering or rolling at a white heat. 

Double Sliear Steel. — Made in the same manner as shear 
steel, only the process is repeated two or more times. 

Alloy Steels 

It has been found that by the addition of some of the rarer 
elements to the compound of iron and carbon very valuable 



38 



MATERIALS 



properties are imparted to that metal. The elements chiefly 
used in alloying are chrome, manganese, molybdenum, 
nickel, silicon, tungsten, and vanadium. One very high class 
of alloy steel, greatly used in the manufacture of lathe tools, 
is said to have the following composition : — 

Carbon . 0-68 per cent. Tungsten . 18-0 per cent. 
Chromium. 5-75 ,, Manganese. 0-09 ,, 

Vanadium . 0-30 ,, Silicon . . 0-46 ,, 

Bessemer Steel 

The Bessemer process of making steel was patented in the 
year 1855 by Sir Henry Bessemer, and is a method by which 
air is blown through a molten mass of pig iron, whereby the 
carbon, silicon, and manganese are burnt out, sufficient heat 
being produced during the process to keep the metal in 
a liquid state and enable it to be poured into ingots. The 
required amount of carbon being added in the form of ferro- 
manganese, a variety of iron rich in carbon and manganese. 

The Bessemer converter is a pear-shaped vessel lined with 
fire-brick, ganister, or dolomite, and constructed to rotate on 
trunnions, through one of which the air is blown. At the 
bottom of the converter a number of water-jacketed tuyeres 
are arranged to convey the air blast to the molten iron. 

Before being run into the converter, pig iron free from 
phosphorus and sulphur is melted, and the inside of the 
converter prepared to receive it. When ready, the converter 
is rotated to the horizontal position, and the molten metal 
poured in from a ladle ; air is then blown in for about 
twenty minutes. The metal during conversion really passes 
through three stages. In the first stage the air blast causes 
a shower of sparks with very little flame, and lasts for about 
four minutes ; in that period the uncombined carbon is con- 
verted to the combined form, and the silicon is changed to 
silica. In the second stage the temperature rises, and for about 
ten minutes the whole mass appears to boil, this being due to 
the oxidization of the carbon and the escape of carbon 
monoxide, CO. In the third stage the air- pressure is 
reduced, and the remainder of the carbon and manganese is 
burnt out. The whole process of conversion takes about 
twenty minutes, and is indicated by a subsiding of the flames. 
The metal is still in the liquid staRC, and the converter is 
then brought to the horizontal position, when the necessary 
amount of carbon is added in the form of spiegeleisen, which 
is white iron containing a known proportion of carbon and 
manganese. The steel is then poured into a ladle, and from 



MATERIALS 



39 



the ladle into iron ingot moulds, whence it goes to the soaking 
pits for about one hour, finally being run through the cogging 
mill, and rolled into bars, angles, tees, plates, etc. 

Blister Steel 

Tbe production of blister steel by the Cementation process 
is the most important preliminary process employed in the 
manufacture of crucible cast steel. To produce blister steel 
by the Cementation process best selected bars of wrought iron 
are placed in a cementation furnace surrounded and packed 
in with charcoal, the furnace fire is lit, and in two days tlie 
conversion of the iron begins. A temperature sufficient to 
keep the bars at a blood-red heat is maintained for about nine 
days, the actual time being determined by the percentage of 
carbon required in the iron, and which ranges between 0-6 
and 1-6 per cent. 

At the end of the heating period the fire is withdrawn and 
the bars taken out, when they are found to bo covered with 
blisters. The bars are broken into short pieces, piled, re- 
heated, treated with a flux of borax and sand, and then 
welded together and drawn into bars ; it is then called single 
Bheu steel. 

When a better quality steel is 'required 'the single shear bars 
are broken into short lengths, selected for fracture, and linn 
piled, reheated, welded, and drawn, and is then called double 
Bheai steel. 

Crucible Steel 

Tool steel, or what is sometimes called cast steel, is 
generally made from blister steel by cutting tbe bars into 
small pieces and melting them in a fireclay crucible, adding 
the necessary amount of carbon in tbe form of ferro-manganese. 

Another method of making cast steel, or alloy steel, is to 
take small pieces of best Swedish bar iron and melt it in air- 
tight crucibles, adding oxide of manganese, charcoal, and any 
other elements required. The steel is run into iron moulds, 
forming ingots, which are hammered into bars or rolled into 
sectional shapes. 

Open Hearth Steel 

Several methods of producing open hearth steel are in vogue, 
the general principle being that a certain quantity of pig iron 
is melted in a reverberatory furnace, and red hematite added 
to oxidize the carbon, silicon, and manganese. Carbon then 
being added in the form of spiegeleisen and ferro-manganese. 



^0 MATERIALS 

It is somewhat similar to the process of puddling wrought 
iron, only on a larger scale. The furnaces have a capacity of 
30 to 50 tons, and are heated by gas made from bituminous 
coal. The air and gas are passed through regenerative 
chambers before being allowed to enter the combustion 
chamber, and are heated to a temperature of about 1,200° Fahr. 
This preheating of the air and gas allows of an extremely 
high temperature being maintained in the furnace, and 
thereby keeps the metal in a liquid state. 

The charge of molten metal has mixed with it red 
hematite ore or other oxides, which, owing to the chemical 
reactions, keep the molten iron in a continuous state of 
agitation. In the open hearth process it is usual to make use 
of scrap wrought iron or scrap steel, because the high 
temperatures obtained by the regenerative furnace allows of 
their being brought to a molten state. If the scrap contained 
too much phosphorus, then burnt lime is added to the 
charge, and when lime is used in order to keep the slag basic 
the process is called the " Basic process ". 

To melt a 30 ton charge of open hearth steel takes about 
five hours. 

Malleable Iron 
To produce a malleable iron casting, the casting is first cast 
in the ordinary manner from hard brittle white iron. The 
Band adhering to it is thoroughly removed by pickling. It is 
then packed in a cast-iron box with powdered red hematite 
ore, or rusty steel turning, then covered with fireclay, and 
brought to a blood-red heat, being kept at that temperature 
from two to seven days. The oxygen of the ore combines 
with the carbon in the iron, and reduces the carbon to less 
than 1-0 percent. Malleable castings can be bent, but they 
cannot be forged in a similar manner to wrought iron. 

Non-Ferrous Metals 

Aluminium. — A metal used chiefly on account of its light- 
ness ; it has a specific gravity of 2-56, and weighs about 
009 lb. per cubic inch. It is of bluish-white colour, and is 
seldom made use of in its commercially pure state. Aluminium 
resists the action of salt water much better than iron or steel, 
and does not con-ode. 

Antimony. — A white metal with a melting-point of about 
1,150° Fahr. It is very brittle, and is chiefly used for hardening 
anti-friction metals. 

Bismuth.— Grey-white in colour. Crystalline and brittle, and 
expands in solidifying. Melts at 520° Fahr. Sp. gravity 9 • 8 



MATERIALS 



41 



Copper. — A pink-coloured metal with a melting-point of 
about 1,900° Fahr. and a specific gravity of 8-82. It is very 
malleable, of high tenacity, and quickly becomes hard and 
brittle in working. When near its melting-point it is extremely 
brittle, and under the influence of sulphur, bismuth, or 
antimony, it deteriorates to a large extent. It is a very good 
conductor of heat, and for that reason is used in the manu- 
facture of locomotive fire-boxes, etc. Its chief use is as 
a constituent with tin and zinc, in forming alloys. 

Lead. — A blue-grey metal with a specific gravity of 11-37. 
It is highly malleable, can be rolled into sheets or formed into 
tubes or pipes. Owing to its low tenacity of 1-5 tons per 
square inch, it cannot be drawn. It is largely used as a 
constituent in the making of bronzes and fusible alloys. 

Nickel. — A yellowish-white metal of about the same strength 
as copper, less ductile but harder. It melts at a temperature 
of about 2,600° Fahr., and in its pure state is very difficult 
to cast owing to the gas given off in cooling. Used to a 
considerable extent as a constituent in alloys of steel. 

Tin. — A white-coloured metal with a yellow tinge and 
a melting-point of 445° Fahr. It is very soft and malleable, 
and can be rolled into very thin sheets. Seldom used in its 
pure state, but forms a valuable constituent in bronzes and 
special alloys. 

Zinc. — A white metal with a greyish tint, melting at 
785° Fahr., and having a specific gravity of 7-1. It can be 
rolled at a temperature between 212° and 300° Fahr. Largely 
used as a constituent in copper alloys. 



Strength and Properties of Metals 
Definition of Terms 

Compression. — A term used to indicate the state the particles 

of a body are in when a force tends to crush the particles 

together. 
Ductility. — A metal is said to be ductile when it can be drawn 

and extended by a tensile or pulling force. 
Elasticity. — The power of a metal to return to its original 

shape after a force has been applied and then released. 
Elastic Limit. — If a metal is subjected to a gradually increasing 

strain, a certain limit is reached within which the 

stresses are proportional to the strains. 
Elongation. — The amount a piece of metal stretches between 

two fixed points is called the elongation. It is made 



42 



MATERIALS 



up of two parts, one due to the general stretch, the 
other to the contraction at the point of fracture. 
Expansion.— Expansion is usually expressed as a coefficient, 
and which is the amount every unit of length expands 
for every degree of rise in temperature. 
Fusibility.— The property of becoming liquid on the applica- 
tion of heat is termed the fusibility of the metal. 
Hardness.— Hardness is the power of the surface of a metal 
to resist penetration by cutting or scratching. It can 
be expressed in relative terms. 
Heat Conducting.— The property possessed in varying degree 
b . v metals for transmitting heat along or through them. 
Malleability.— The changing of the shape by hammering, 

pressing, or rolling without causing fracture. 
Sheanng.— The shearing strength of a metal is equal to the 
force which, if applied at right angles to the line of 
axis, would cause the parts to separali:. 
Specific Gravity.— The ratio of a volume of metal to the 
weight of an equal volume of water is termed the 
specific gravity. 
Specific Heat.— The relative amount of heat absorbed by 
metals, compared to the heat absorbed by an equal 
quantity of water when raised through "the same 
temperature. 
Tenacity.— The tenacity of a metal is the power to resist the 

effort of stretching or pulling apart. 
Tensile Strength.— The equivalent to the amount of force 
applied to a piece of metal in a line with its axis, to 
just overcome the cohesion of particles and pull it into 
separate pieces. 
Toughness.— k metal is said to be tough when it can be bent, 
first in one direction, and then in the opposite, without 
developing a fracture. 
Weldability. — The property possessed by a metal which 
renders it capable of being joined when in a state 
of fusion. 



The Relative Hardness of Metals 

Brincll Method 

Wrought iron . 14-5 

Mild steel . 20-0 

Cast iron (soft) 24-0 

Cast iron (hard) 35-0 

Steel (hardened) 93-0 



Lead 


10 


Tin . 


2-5 


Zinc . 


7-5 


Copper (soft) 


80 


Copper (hard) 


120 



MATERIALS 



48 



Order of Malleability of Metals by Hammering 

1. Aluminium. 5. Lead. 

2. Copper. 6. Zino. 
8. Tin. 7. Iron. 
4. Platinum. 8. Nickel. 

Composition of Alloys 
Percentage 





Copper 


Zino 


Tin 


Manga- 
nese 


Phos- 
phorus 


Alu- 
minium 


Admiralty 

metal 
Brass . . . 

Bronze, 

phosphor 
Bronze, 

manganese 
Bronze, 

aluminium 
Gun-metal . 

Muntz metal 

White metal 


75 
66 
90 
60 
90 
88 
60 
70 


25 

34 

8 

38 

2 

40 
26 


2 
1 

10 

4 


0-3 


0-3 


0-5 
10 



Allowance for Contraction 

All the common metals expand when heated and contract 
in cooling, and it is owing to the expansion and contraction of 
metals before and after cooling that patterns used in the 
foundry are made larger than the required casting. The 
allowance is expressed as so much per foot. The following 
figures give approximate allowances, but considerable judgment 
is required in order to decide the exact amount suitable for 
a particular job. 



per ft. 
Cast-iron large castings ^j in. 

,, small castings -fa in. 

,, pipes . Jin. 

Castings in sino . A in. 

„ tin - iin. 



per (t. 

Cast-iron girders . A in. 
Castings in brass (large) ^j in. 

,, ,, (small) | in. 

,, copper . i^in. 

„ lead . A in. 



44 MATERIALS 

Order of Ductility of Metals in Wire Drawing 

1. Platinum. 5. Nickel. 

2. Iron. 6. Zinc. 
8. Copper. 7. Tin. 
4. Aluminium. 8. Lead. 

Ultimate Strength of Metals 



Metal 



Aluminium 

Brass, common... 

Bronze, manganese 

Bronze, phosphor 

Copper, cast 

Copper, rolled 

Iron, cast 

Iron, wrought 

Lead 

Steel castings 

Steel wire 

Tin 

Zino 



Ten«ion 
lb. sq. in. 



15,000 

22,000 

60,000 

58,000 

24,000 

86,000 

15,000 

48,000 

2,000 

70,000 

160.000 

3.500 

5,000 



Compression 

lb. ■-'{. in. 



12,000 

30,000 

120,000 

40,000 
58,000 
80,000 
46,000 

70,000 

6,000 
20,000 



8bear 
lb. sq. in. 



12,000 
36,000 



30,000 

18,000 
40,000 

60,000 



Approximate Weight of Metals 



Aluminiurr 
Antimony . 
Brass . . 
Copper . . 
Iron, cast . 



lb. 
009 
0-24 
0-30 
0-31 
0-26 



■per Cubic Inch 



Iron, wrought 
Lead . . . 
Nickel . . . 
Platinum . 
Silver . 



lb. 
0-28 
0-41 
0-31 
0-fiO 
0-38 



Steel 
Tin . . 
Tungsten 
Van ikI ium 
Zinc . . 



lb. 
0-28 
0-26 
0-67 
019 
0-26 



Melting-point of Mktals 



Aluminium 
Antimony 
Brass . 
Bronze . 
Copper . 
Iron, cast 
Iron, wrought 
Lead . , . 



Fiilir. 
1,218° 
1,160° 
1.750' 
1,670° 
1,910° 
2,300° 
2,900° 
620° 



Nickel . , 
Platinum 
Silver . , 
Steel . . 
Tin . . 
Tungsten 
Vanadium. 
Zinc . , 



Fahr. 
2,800° 

3.200° 
1,750° 
2,500° 

440° 
5,400° 
3,200° 

780° 



MATERIALS 



45 



Weight of Hound and Square Barb of Wrought Iron 

in PoutuL* per Foot 

(For Steel add 2 per cent.) 

Thii-kneRS or diameter Weight of one foot Weicht of one fool 

of metal in inches of square iron of round iron 

£ 0-05'J 0041 

! 0-208 0164 

0-469 0-368 

0-H33 0-654 

11-302 1023 

1-875 1-473 

2-553 2004 

3-333 2-618 

4-219 3-313 

5-208 4-091 

6 302 4-950 

7-500 5-890 

8-802 6-913 

10-21 8018 

11-72 9-204 

13-33 10-47 

1505 11-82 

16-88 13-25 

18-80 14-77 

20-83 16-36 

•22 97 1804 

25-21 19-80 

27-55 21-64 

3000 23-69 



Salt Batiis for Hardening Purposes. 
Pure Barium Chloride, 2000° to 2400° F. 



Barium Chloride, 3 parts \ 



1400° to 1650° F. 



Potassium Chloride, 2 partsj 

Potassium Nitrate, 1 P«*t\ 560 . fco ]075 „ F 

Sodium Nitrate, 1 part J 



THE HEAT TREATMENT OF METALS 



47 






Chapter IV 
THE HEAT TREATMENT OF METALS 

Annealing 

The process of manufacture required to produce bars of 
steel, castings of steel, or forgings of steel must naturally set 
up some internal or external strains. All drawing, twisting, 
forging, rolling, bonding, and welding operations tend to 
set up stresses, which, to a greater or less degree, cause 
brittleness. 

To reduce the stresses and restore the metal to its normal 
condition, and at the same time soften it, it is necessary to 
put it through one of the annealing processes and thoroughly 
anneal it. 

It is specially desirable that high carbon steel tools, which 
may require to be hardened after manufacture, should be 
annealed, and the necessity becomes greater when the metal 
is of intricate shape, or when holes of irregular shape pass 
through it. 

The methods of annealing differ to some extent with the 
class of work requiring annealing. The ordinary shop method 
for annealing a small job is to bring the piece to a blood-red 
heat and place it in the hot ashes of the forge to gradually 
cool. This rough and ready method is suitable for some work, 
but should never be adopted for the more intricate work with 
carbon steels. For this class of work a cast-iron box is 
obtained, and the piece of work to be annealed is placed in 
and packed all round with charcoal, care being taken that 
it is evenly packed with not less than one inch of charcoal 
surrounding every part. The whole is then placed in a gas 
oven and brought to a temperature of 1,450° Fahr., corre- 
sponding to a cherry-red colour ; it is kept at that temperature 
about one hour, after which the whole is allowed to gradually 
cool, and on no account must the work be taken out of the 
box until it is quite cold. 

In annealing wrought or cast iron the same method is 
adopted, but in the place of the charcoal, cast-iron turnings 
can be used if desired. 

Copper and Copper Alloys.— When copper is worked in any 
way it very quickly becomes hard and brittle, and during the 



process of such operations as flanging or bending it is necessary 
to constantly anneal the metal. 

The annealing of copper is a very simple operation ; the 
metal is brought to a blood-red heat in a clean charcoal fire, 
and then plunged into cold water. Care must be taken not to 
overheat the metal, and the water used must be clean and 
quite free from grease. 

Hardening Steel 

Carbon can be found in steel in two forms, one known as 
pearlite or softening carbon, the other as cementite or 
hardening carbon. All varieties of carbon steel containing 
more than -5 per cent of carbon can be made hard by bringing 
it to a certain temperature and then suddenly quenching in 
water. The temperature to which steel must be brought 
in order to bring about this change in the nature of the 
carbon is known as the point of decalescence. 

It is found that steel slowly cooling from a high temperature, 
at a certain point, actually increases in temperature in spite 
of its surroundings being colder ; this is the point where the 
carbon changed its form, and is the recalescence point. 

It is also found that when a piece of steel has been heated 
to a certain point, it continues to absorb heat without showing 
a corresponding rise in temperature; this is called the point 
of decalescence. The decalescence point is from 100° to 
200° Fahr. higher than the recalescence point. 

To harden a piece of carbon steel it is necessary to bring 
it, first, to the point of decalescence, which corresponds to 
a temperature of about 1,450° Fahr., and then cool it suddenly 
before it reaches the point of recalescence, which corresponds 
to a temperature of about 1,280° Fahr. 

Tempering Steel 

The object of tempering is to bring a piece of metal or a tool 
to a known degree of hardness, suitable to the requirements of 
the tool or part, for the work it may have to do. 

The more heat imparted to the part during the tempering 
process the more the hardness will be reduced. 

When a piece of hot steel with one face or edge made 
bright is exposed to the atmosphere, it will be found that 
various colours appear on the metal. These colours are 
caused by the formation of thin films of oxide, and are due 
to the action of the oxygen in the air and the carbon and 



48 TIIE HEAT TREATMENT OF METALS 

heat in the metal. Each colour corresponds with a fixed 
temperature, which is shown in the following table: — 

Temperature Table 



Colour Approx. Temp. 


Colour Approx. Temp. 




Degrees !•'. 




Degrees F. 


Light straw 


430 


Red . 


. 1,080 


Straw . 


450 


Dark red 


. 1,300 


Dark straw 


490 


Cherry red . 


. 1,450 


Yellow . 


500 


Bright cherrj 


. 1,800 


Brown purple . 


530 


Light orange 


. 2,000 


Dark blue 


580 


White . 


. 2,400 


Full blue 


600 


Brilliant white 


. 2,550 


Greenish blue 


630 


Dazzling white 


. 2,730 



The methods adopted for tempering differ very greatly, and 
depend upon the class of steel, the size, and the nature of the 
work the piece of metal will be called upon to do. Two 
distinct methods are in use, one in which the work is first 
fully hardened and afterwards tempered, the other in which 
the hardening and tempering are done in one operation. 
The first method is generally adopted for high-class tool steel 
and intricate work, and the second for ordinary carbon steel 
cutting tools. In the former method the piece to be hardened 
and tempered is first hardened to the full extent, and then the 
temper is drawn by placing it in a bath of metal previously 
brought to the required temperature, or by holding it close to 
a flat piece of red-hot iron. 

In the latter method the piece to be hardened and tempered 
is brought to a cherry-red about three inches, the end is then 
placed in water for about half this distance and cooled ; one 
face is immediately rubbed with a piece of brick, and as the 
heat remaining in the metal conducts itself towards the one end 
the colours can be seen approaching. When the desired colour 
or temperature reaches the end, further reduction can be 
stopped by plunging it into cold water. 

Alloy Steels. — The introduction of alloy steels in the shape 
of self-hardening and high-speed steels has altered the older 
methods of hardening and tempering. Many of the special 
tool steels require a special hardened method, and it is 
always advisable to consult the maker as to what is the correct 
method. 



THE HEAT TREATMENT OF METALS 



49 



Mnshet and tungsten steels are hardened by heating the 
cutting edge slowly to a bright red, and then rapidly to 
a white, cooling off in a blast of cool air, or plunging into 
cold oil. The following table gives the colours to which 
various tools should be tempered : — 

Colours for Tkmpkiung 

Colour Tools to be Tempered 

Light straw . Scrapers, scribers, lathe tools. 

Dark straw . Chisels, drills, drills, screwing tackle. 

Brown purple Hack saws, fiat drills, wood tools. 

Dark blue . . Springs, screw-drivers, wood saws. 

Greenish blue . Too soft for most purposes. 

Case-hardening .— Case-hardening is a process wherobv the 
skin of mild steel or wrought iron is converted into a form of 
carbon steel. The small percentage of carbon in mild steel 
does not allow of its being hardened, but. by taking iidvuiituge 
of the case-hardening process it is possible to add sufficient 
carbon to allow the piece to be hardened. 

The quickest method of case-hardening is by menu-; of 
potassium ferro-cyanide. The cyanide is first crushed in 
a tray or melted in a ladle ; the metal to be hardened is 
brought to a cherry red, and rolled in the powder or placed 
in the bath of liquid cyanide, after which it is plunged into 
cold water. 

Various compounds are used for case-hardening, all of 
which contain in some form a carbon substance ; the com- 
monest of these substances are bone, charcoal, leather, and 
blood. 

To case-harden castings of unequal form, the best material 
is perhaps granulated raw bone. The process requires the 
use of an iron box in which the metal is packed, surrounded 
by the bone. The whole is then placed in a gas oven or 
furnace, and kept at a cherry-red temperature for a period 
varying between two and twenty hours, after which the whole 
is plunged into cold water. By this means it is possible to 
case-harden from g^ to J of an inch in depth, but little 
advantage is gained by going deeper than £ of an inch. 



Chapter V 



COMMON WORKSHOP TOOLS 

It is proposed in this chapter to deal with common 
engineering workshop tools in everyday use, and to indicate 
the name and the purpose of each tool. 

Rules. — Engineers' steel rules are made in an infinite 
variety of lengths, widths, and thicknesses, both hardened 
and flexible. The usual graduations are 64ths, 32nds, 16ths, 
and 8ths, but miy number of graduations of the inch can be 
either obtained or specially made. A most useful set of 
graduations are lOOths, oOths, and lOths. 

When metric measurements are to be made, then a rule 
graduated in millimetres and centimetres is used, and as this 
is a frequent occurrence, rules are sold with millimetre 
graduations on one side and English measure on the other. 

For accurately dividing rules special machines are used, 
and all reputable makers can be relied on to supply a rule of 
sufficient accuracy for all practical work. 

Calipers. — Calipers of the ordinary type are not measuring 
tools, they are used simply to obtain a length, the actual 
measurement of which must be taken by some form of 
measuring instrument. An enormous variety of calipers are 
on the market ; the best form perhaps are those in which the 



Fig. 44. 



Pig. 45. 





COMMON WORKSHOP TOOLS 



51 



legs are opened and closed by means of a spring, the adjust- 
ment being made by a knurled nut. The simplest form of 
calipers ai'e those used for inside and outside calipering, these 
are illustrated in Fig. 44 (outside calipers) and Fig. 45 (inside 
calipers). For special work, such as screw-cutting, calipers 
with suitable shaped ends are used ; these may be very broad 
for taking the tops of external threads, or very thin for going 
to the bottom of threads, or, if for internal screw work, then 
with the ends coining to a point. 

Using Calipers 

Considerable practice is required before it is possible to 
caliper with any great degree of accuracy, especially when 
using the inside caliper. If it is desired to caliper a shaft 
held between the centres of a lathe, then proceed as follows : 
Hold the caliper by means of the thumb and first finger, witli 
the second finger between the legs, keeping the caliper exactly 
vertical, adjust and test it on the work ; when it passes over 
of its own weight, and at the same time can be felt to touch, 
it is set correctly. 

When using the inside caliper, one of the legs should be 
kept stationary, and with the other leg two small arcs should 
be made, first in a line with the hole and then at right angles 
to the hole; this will allow of the caliper being adjusted to 
the maximum size ; for finer adjustment the caliper can be 
moved up and down the hole. 

Fig. 46. 



Dividers. — This tool is illustrated at 
Fig. 46. The points are hardened and 
tempered, and the tool is used for exactly 
the same purpose in workshop practice 
as the compasses are used in the drawing 
office, that is, marking out circles, arcs, 
and finding centres. When striking 
circles or arcs on metal with the dividers 
it is usual to make a very light centre dot 
mark for the fixed leg of the dividers to 
work in. 




52 



Fio. 47. 



Fig. 48. 






COMMON WORKSHOP TOOLS 



Scribers. — In order to mark/ihe surface 
of metal, scribers made from oast steel 
with the ends pointed and hardened are 
used. In most cases the straight scriher 
can be used, but often it is not possible 
to make the straight scriber do, in which 
case the pointed end can be turned round 
to form a bent scriber. The straight and 
bent scriber are illustrated at Fig. 47. 

When the surface of the metal to be 
marked is polished or very bright, or 
when a scratch is objectionable, then a 
scriber made of brass can be used. 



Centre Punch. — A tool made from cast steel, 
generally of hexagonal or octagonal section, one 
end being turned to an angle of 60°, witli the point 
hardened and tempered. This tool is used for 
lining out work previous to maohining and fitting. 
The dots made by the punch should be light, abort 
i" or J" apart, and exactly on the line bo that when 
the machining is finished half the dot will be left in 
the work. This tool is shown at Fig. 48. 



Pin Punches. — Made somewhat similar to the centre punch, 
one end bcinj,' turned to the desired diameter and length, the 
end being left flat. This tool is used for driving out taper and 
split pins and for work of a similar character. 

Fio. 49. 

Try Square. — The best try squares are 
made from one piece of steel, machined to 
size, hardened, and then accurately finished 
by grinding. This important tool is used 
for testing the accuracy of two surfaces at 
right angles to each other, or for marking 
out work on the lining out table. It is 
shown at Fig. 49. 



COMMON WORKSHOP TOOLS 



53 



Thickness Gauge.— The thickness gauge generally takes 
the form of a small case containing a number of pieces of 
steel of a definite thickness, the actual thickness of each blade 
being shown in thousandths of an inch. The blades of metal 
can be used separately or collectively in testing the distance 
between two surfaces, or for obtaining clearances between two 
fixed parts of a machine. 

Surface Plate. — A cast-iron plate with the face and edges 
accurately machined, and afterwards scraped by hand as near 
true as it is possible to make it. It is used for testing the 
flatness of a piece of work. When testing a job the surface 
plate is first very lightly rubbed over with a little blacklead or 
redlead and oil. and the piece of work to be tested is rubbed 
on the surface, the transference marks showing the high 
places. 

Radius Gauge. — This tool consists of a number of pieces 
of steel held in a case, each piece having a definite radius at 
the end, and which may be either internal or external. The 
actual size of the radius is stamped on each piece of metal. 
It is used for testing the radius of a piece of work, or for finding 
the exact size of a radius. 

Marking-off Table.— All engineer shops contain a marking- 
off table. It consists of one or more cast-iron blocks mounted 
on legs, the faces of which have been machined flat and the 
edges square. The size of the table depends upon the class 
and size of work dealt with, and as the name implies it is 
used for lining or marking off work previous to machining. 

Vce Blocks. — Vee blocks are made in pairs from oblong 
blocks of cast iron, a vee being cut out having an angle of 90°. 
These tooUs are used for lining out or centering round shafts, 
the metal being rotated in one or more vee blocks as required. 

Hack Saws.— When metal is to be cut by hand power the 
hack saw is used. This tool consists of some form of frame, 
constructed to hold a renewable saw blade. 

Scribing Block.— The scribing block or surface gauge is 
made in a variety of forms. It is a tool used for scribing 
lines at a given height from some face of the work or the 
continuation of lines around the several surfaces. The best 
form of surface gauge consists of a heavy base and upright to 
which is attached a scriber held by a clamp, which may be 
turned through a complete revolution. By resting both 
the surface gauge and the work upon a plane surface such 
as a surface plate it is possible to set the point of the scriber 
at a given height, either by use of a rule or some form of 
height gauge, and draw lines at this height on all faces of the 



54 



COMMON WORKSHOP TOOLS 



Pig. 50. 



-i i 



work, or on any number of pieces when 
duplicate parts are being made. 

A simple form of surface gauge is 
illustrated at Fig. 50, the ends of the 
scriber being straight and bent as shown. 
The use of the surface gauge is not con- 
fined to scribing on vertical surfaces only, 
it may be used on other surfaces or as 
a height gauge as well. The bent end 
on the scriber permits lines to be drawn 
on horizontal surfaces. 

It is necessary in some cases to prepare 
the surface of the work so that the line 
made by the scriber will be sufficiently 
clean-cut to enable the workman to dis- 
tinguish it quickly. This is done in the 
ease of rough castings by chalking the 
surface and rubbing in with the finger. 
In the case of a highly finished surface 
some other method is necessary. The 
usual way is to use a solution containing 
copper sulphide and nitric acid in the 
proportions of one ounce of copper sulphide, four ounces 
of water, and a teaspoonful of acid. This solution gives 
a reddish-brown colour against which the lines will show. 

too. 51. 

Bevel Gauge. — The simplest form 
of bevel gauge is a tool similar to that 
illustrated at Fig. 51 ; it is used for 
transferring angles and for testing and 
marking off angles. It is constructed 
in a variety of shapes and forms, and 
requires to be set to the desired angle 
either by means of a protractor, from 
a standard gauge, or from the work it is intended to copy. 

Fia. 62. 

Depth Gauge. — The depth gauge 
is a tool, used as the name implies, 
for testing the distance between 
two surfaces, finding the depths 
of holes, and work of a similar 
character. Made in a large variety 
of forms, sometimes consisting of 
a narrow rule fitting in a cross-bar in such a manner as to be 




© 



U 



COMMON WORKSHOP TOOLS 



55 



adjustable ; this tool is shown at Fig. 52. When great 
accuracy is required, it is fitted with a vernier attachment, by 
means of which it is possible to measure to thousandths of 

11,1 Screw Cutting Gauge.— Screw cutting gauges are made for 
testing the tools used in cutting acme, vee, and square threads. 
They consist of fiat pieces of steel, with pieces of the exact 
size of the thread cut out. ,, ..; . 

Wire Gauge— A tool used for measuring the thickness of 
sheet metal. Cuts are made in the gauge of various thick- 
nesses, each cut corresponding to a fixed and known size, the 
amount being stamped on the gauge. 

Tapping and Drill Gauge.-This most useful tool is used 
for testing drills and round metal ; it gives at once both tapping 
and drilling sizes, and is a great time-saver. It consists of 
a piece of hardened metal with two or more rows of holes 
of exact gauge at tapping size, each size being stamped in the 

ga S«eo< Rules.— It is impossible to hold the ordinary steel 
rule on a cylindrical shaft and keep it parallel, and to over- 
come this difficulty, rules with flanges similar in shape to 
angle bars, are used. The two edges of the rule form a box 
square when applied to a round piece of work, and permit a 
line or lines to be drawn parallel with its axis. 

Centre or Screw-Cutting Gauges.— These useful little tools 
are used in grinding and setting screw-cutting tools 

Screw Pitch Gauges.— -These consist of a number of Bpnng 
temper leaves having sections of various ^dard screw 
threads The leaves are stamped with the pitch or threads 
per inch, and are used to determine the actual pitch oi a 

81 Zfe T &iuge.— This gauge contains a number of leaves 
the ends of which are ground to an angle It is a very con- 
venient tool and frequently can be used in place of the 
protractor, saving considerable time. 

Contraction Rule.— These rules are graduated in a similar 
manner to the ordinary rule, but allowance is made for 
various degrees of contraction. 



Chapter VI 



MEASURING TOOLS AND GAUGES 

It is intended in this chapter to deal with fine measuring 
tools and gauges, or tools by means of which it is possible to 
measure to finer limits than with the ordinary rule. 

The commonest form of measuring tool is, of course, the 
engineers' rule, and the unit of measurement for the greater 
part of the work done in the United Kingdom is the Standard 
Imperial Yard. 

With (he ordinary rule it will be found difficult to measure 
accurately to a smaller limit than g^ of an inch ; many rules 
are, however, graduated to ± fo of an inch, and it is certainly 
impossible to take readings smaller than } j of an inch on the 
ordinary rule. 

The Micrometer 

The micrometer caliper is an indispensable tool where very 
accurate measurements are required. It is constructed in 
several different shapes and forms, the measuring points in 
particular being formed to suit the special class of work on 
which it is to be used, and which may be for the purpose 
of measuring the depths of threads, the diameter of a piece of 
work, the size of a hole, or for some special purpose requiring 
specially designed anvils. 

Principle of the Micrometer 

Before the novice starts to study the working of the micro- 
meter, he must first perfectly understand the meaning of the 
word pitch, as applied to a screw thread. This can be done 
to the best advantage by taking a screw and nut, and actually 
demonstrating that the nut, in one complete revolution, will 
move a distance equal to the pitch of the screw, that is to say, 
if the screw has sixteen complete threads per inch, then the 
nut would move in one complete revolution a distance of 
fa of an inch. It should also be proved that a nut turned 
half a revolution moves a distance equal to half the pitch, also 
that whatever fraction of a complete turn the nut is moved, 
so the distance will equal that fraction of the pitch. 

Example. — If a screw thread has twenty complete threads 
in one inch, then the pitch is fa of an inch, and if the nut is 



MEASURING TOOLS AND GAUGBS 



57 



moved fa of a turn, then the distance moved would be fa of 
fa — 2&u> or '* tne nut wa:3 turnca 5V 0111 turn the distance 
moved would be fa of fa = ^n OI in inch. 

Outside Micrometer Caliper 

A micrometer graduated to read to nftnj of Rn incn ia 
illustrated at Fig. 53. The screw thread is quite enclosed and 
thus rendered dust-proof. The wearing parts are hardened, 
Fig. 63. 



AmiU Screw IMBarn 



Thimble or 
Sleeve 




and provision is made for taking up the wear. The various 
parts are named in the illustration for convenience of reference. 

The pitch of the screw is forty complete threads to one inch, 
or fa of an inch. The graduations on the barrel in a line 
parallel to its axis are forty to one inch, and thus they agree 
exactly with the pitch of the screw ; they are numbered at 
every fourth division, 0, 1, 2, 3, 4, etc. As these graduations 
conform to the pitch of the screw, each division must equal the 
longitudinal distance traversed by the screw in one complete 
revolution, and shows that the micrometer has been opened ox- 
closed fa or TtMhr o r "0 2i5 °* ,in incn - 

The bevelled edge of the thimble or sleeve is graduated into 
twenty-five parts, and figured every fifth figure, 0, 0, 10, 15, 20. 
Each division, when coincident with the line of graduations on 
the barrel, indicates that the screw has made fa of a revolution, 
and the opening or closing of the caliper increased or decreased 
fa of fa = rib« or -04 X -025 = -001. 

To read the Caliper 
Before proceeding to read the micrometer, particularly note 
the following : — 

1 division on the barrel equals -025 

2 .. „ ., 05 
8 .. .. .. -075 

4 1 



58 



MEASURING TOOLS AND GAUGES 



Thus every fourth division equals a certain number of tenths. 
Also note that each division on the thimble represents a 
movement of -001 of an inch. 

To read the caliper, first read the numbers of tenths, then 
the number of fortieths coming after that figure, then the 
thousandths. 

Taking Fig. 54 as an example, the reading would be: — 

Pig. 54. 5 tenths = -5 

1 fortieth = -025 

15 thousandths = -015 

•540 




The Vernier 

The vernier is a device invented by an Italian named 
Pierre Vernier in the year 1631, and is used in measuring 
instruments for subdividing the divisions of a scale into finer 
divisions, these smaller divisions being too fine for reading in 
the ordinary manner. 

The scale of the fixed portion of Pig. 55 is graduated in 
fortieths of an inch or -025, every fourth division being figured, 
and representing a certain number of tenths. On the sliding 
vernier a length equalling twenty-four divisions on the fixed 
scale is divided into twenty-five equal parts ; thus the width 
between one space on the vernier is less than the width between 



Fio. r.5. 

. Scale. 
/ 2 3 \4 5 

iliilll iullllljjjjjjjj.l.1.1 



fTTT] 
S 10 IS 20 2S 



lll.MII|Tllllll. 



Vernier. 

one space on the main scale by ifa of fa, which equals ^^tns or 
-001 of an inch. If the zero mark on the vernier is set to 
coincide with the zero mark on the scale, then the next two 
lines will not coincide by x^tnr of an inch ; the next two lines 
will be T&5T5 apart, the next two will be t riW> an d so on until 
the last two lines will be found to exactly coincide. 

To read the Vernier 

To read the vernier first read the tenths, then the fortieths, 
then the thousandths as indicated by the coinciding figure on 



MEASURING TOOLS AND GAUGES 



59 



the vernier. In the example shown at Fig. 55 the reading 
would be — 

1 inch 10 

2 tenths = *2 
fortieths = '0 

6 thousandths on vernier = "006 

1-206 



The Vernier Micrometer 



Pro. 56. 




Sleeve. 



In order to make liner 
measurements than thou- 
sandths of an inch the 
micrometer is constructed 
with a vernier reading ; 
this consists of a series of 
divisions on the barrel of 
the caliper as shown in 
Fig. 56. These divisions 
are ten in number, and 
occupy exactly the same 
length as nine divisions on 

the thimble, and for convenience in reading are numbered 0, 1, 
2, etc., up to 10. The width between two lines on the vernier 
will be less than the distance between two lines on the thimble 
by fa of i^fon, which equals -0001 of an inch. Accordingly, 
when a line on the thimble coincides with the first line on 
the vernier, the next two lines on the right differ from each 
other by fa of lne length of a division on the thimble ; the 
next two differ by fa, and so on. 

To read the Vernier 
When the caliper is opened the thimble is turned to the 
left, and when a division passes a fixed point on the barrel it 
shows the caliper has been opened itAih <>f an inch. Hence, 
when the thimble is turned so that a line on the thimble 
coincides with the second line (end of the first division) of the 
vernier, the thimble has moved fa of the length of one of its 
divisions and the caliper opened fa of njVnr or rnJnrr of an 
inch. When a line on the thimble coincides with the third 
line (end of second division) of the vernier, the caliper has 
been opened njfrnj of an inch, etc. When a line on the 
thimble coincides with the fourth line (end of third division) 
of the vernier, and the reading is rdhnr of an inch, and so on. 



60 



MEASURING TOOLS AND GAUGES 



To read the vernier micrometer, first note the tenths, 
fortieths, and thousandths as usunl, then read the numher of 
divisions on the vernier commencing at 0, until a line is 
reached with which a line on the thimble is coincident. 
If the second line (figured 1), add 1(i hnf'< if the third (figured 2), 
add mflon , and so on. 

The Vernier Sliding Caliper 

The usual type of engineering workshop sliding vernier 
caliper h.is the bar of the instrument graduated into inches 
and numbered 0, 1, 2, etc., each inch being divided into ten 
parts, and each tenth part subdivided into four parts, making 
forty divisions to the inch. On the sliding jaw or vernier is 
a line of divisions, twenty-five in number, and marked 0, 5, 10, 
15, 20, and 25. 

I-'ifi. 57.. 




Tc read the Sliding Caliper 
Note the number of inches, then the tenths, then 
fortieths, and lastly the thousandths on the vernier. 
In Fig. 57 the reading would be 
1-0 
•4 

•025 
•009 



the 



1-434 



The Vernier Bevel Protractor 

A very useful and accurate tool for marking out angles, the 
vernier indicates every five minutes (5') or one-twelfth of 
a degree. 



MEASURING TOOLS AND GAUGES 



61 



Every space upon the vernier is 5' shorter than two spaces 
on the true scale. 

When the line marked O on the vernier coincides with the 
line marked O on the true scale, the edges of the base and 
blade are parallel. When the swivel head is moved so the 
line on the vernier next to coincides with the line next but 
one to O on the true scale, the included angle of the base and 
blade has been changed & of a degree or 5'. 

To read the Protractor Setting 

Head off directly from the true scale the number of whole 
degrees between O and the of the vernier scale. Then 
count, in the same direction, the number of spaces from the 
zero of the vernier scale to a line that coincides with a line on 
the true scale ; multiplying this number by 5 the product will 
be the number of minutes to be added to the whole number of 
degrees. 

t"iG. 57a. 




Example. — As the vernier is shown in Fig. 57a it has moved 
12 whole degrees to the right of the O upon the true scale 
and the 8th line on the vernier coincides with a line upon the 
true scale as indicated by *. Multiplying 8 by 5 the product, 
40, is the number of minutes to be added to the whole 
number of degrees, thus indicating a setting of 12 degrees and 
40 minutes (12° 40'). 



The Metric Micrometer Caliper 

The metric reading micrometer is constructed on exactly 
the same principle as the micrometer for reading in inches. 






62 



MKASIT.ING TOOLS AND GAUGES 



Fig. 58. 

50 Divisions 




Pitch of screw %m.m. 



The pitch of the screw 
is one-half a millimetre 
(J ram.), and the gradua- 
tions on the barrel 1 mm. 
and J mm., the thimble 
is divided into 50 parts, 
thus giving a reading of 
one hundredth of a milli- 
metre. To read the 
micrometer first note the 



number of full millimetres, then see if one-half the millimetre 

shows or not, then note the number of hundredths on the 

thimble. Fig. 58 illustrates the method of graduating ; in 

the example we see 18 millimetres, 1 one-half millimetre, and 

43 hundredths of a millimetre, and which would be 

180 

0-5 

•43 

18-93 

Inside Micrometers 

When linear measurements of internal dimensions of more 
accurate lengths than can be taken with the rule and caliper 
have to be made, then the internal micrometer can be used. 
This instrument consists of a micrometer head graduated to 
read thousandths of an inch or hundredths of a millimetre, and 
is provided with sets of rod of various lengths. By means of 
the extension rods it is possible to measure within the limits 
of the smallest and longest available lengths, the smallest 
length being governed by the length of the micrometer head, 
and the longest by the length of the extension pieces. 

Gauges 

The advantages of working to gauge are so many that 
a great part of modern workshop practice is carried out under 
some system of working to limits. Interchangeability, 
rapidity of production, lessened supervision and inspection, 
the elimination of the human factor in judging sizes, and the 
reduction of the amount of spoiled work, are all factors 
tending to make the use of some means or methods for 
controlling sizes during the process of manufacture of utmost 
importance. 

In a general limit system, that is a system that can be 
applied to all classes of work, it is necessary to decide on 






MKASURING TOOLS AND GAUGES 



63 



what basis Hie limits are to be fixed. In the Hole Basis 
system provision is made in the size of the hole for error in 
workmanship only, and to obtain the quality of fit desired 
variation of size is allowed on the size of the shaft or journal. 
Tin- variation is determined by the requirements of the job. 

To serve as a guide, and to give some idea of the amount of 
tolerances allowable, the following table of running fits is 
"iven A running fit is where a Bhaft is of such a diameter 
that it will revolve quite freely in a hole which it fits, and 
i,.-, .. c- a space for a slight film of oil. Class X is suitable for 
running fits for engine and other work where easy fits are 
required. Class Y is suitable for high speed and good average 
machine work. Class Z for fine tool work. 





Allowances fob 


Running Fits 




Nominal Uptoi 

DiameterB | hi. 


ft-1 

in. 


1,V2 
in. 


aft* 

in. 


8rV4 
in. 


4A-5 
in. 


5A 6 
in. 


Class X ' 
High limit -00100 
Low „ - -00200 

Tolerance ' -00100 


-00125 
-■ 00275 

•00150 


- -00175 
- -00850 

•00175 


- -00200 
-•00425 

•00225 


-•0i250 
-• 00500 

•00250 


-•oonoo 

- -00575 
•00275 


-•00850 
-•00650 

•00800 


Class Y 
High limit 
Low 

Tolerance 


- -00075 - -00100 
-•001251- 00200 

•00050 -00100 


-00125 
-00250 

•00125 


-•00150 
-•00300 

•00150 


-•00200 
-00350 

•00150 


-• 00225 
-•00400 

•00176 


-•00250 
-00460 

•00200 


Class Z 1 
High limit |- -00050 - -00076 
Low --00075 1 - -00125 

Tolerance 1 -00025 -00050 


- -00075 
-•00150 

•0007: 


-00100 
- -00200 

•OO1O0 


-00100 
-00225 

•00126 


-•00125 
-•0025C 

•0012C 


- -00125 
- -00275 

•00150 



It will be seen from the above table that five places of 
decimals are used ; the dimensions, however, actually run in 
thousandths and quarter thousandths. 
Using Gauges 

The fitter or turner is not concerned with the amount of 
tolerance allowed for any particular job. The only question 
for him is the turning or fitting of the work to suit the 

gauges. . 

In using limit gauges, either internal or external, it is 
intended that one end or one part of the gauge should pass 



64 



MEASURING TOOLS AND GAUG1SS 



MEASURING TOOLS AND GAUGES 



66 






over or go in the work, and the other end or part not go in or 

pass over the work. No force must be applied to any gauge, 

and the weight of the gauge alone should be sufficient to carry 

Pig. 59. Pig. 60. 





it over the work. The object to be aimed at in turning to 
limit gauge is to reduce the metal to such a size that the large 
end or plus end of the gauge goes over or in the work, and at 
the same time the work must be of such a size that the minus 
end or small end will not go over or in the work. The correct 
method of holding the external and internal limit gauge is 
shown in Figs. 59 and 60. 

Calipers and measuring tools are entirely dispensed with 
when using limit gauges, and nothing is left to the judgment 
of the workman, except finding the quickest and best method 
for making one end of the gauge pass over the work, and at 
the same time leaving the work of such a size that the other 
end of the gauge will not go over the work. 
Classification of Gauges 
The various gauges used in workshop practice may be 
classified as follows : — 

Standard Internal Gauges 

Standard External ,, 

Internal Limit ,, 

External Limit ,. 

Caliper. 

Standard Taper ,, 

Standard Screw 

Adjustable External ,, 

Adjustable Screw 

Position ,, 



Standard Internal Gauges.— Fig. 61. Usually takes the 
form of a cylindrical gauge ; it is used for the most accurate 
work, possesses large wearing surfaces, and is hardened, 
ground, aud lapped to within -0001 of the correct size. 
Pig. 61. 



Standard External Gauges. — Fig. 61. Made in the form 
of a ring, very accurately finished to within the limit of -0001. 

Internal Limit Gauges. — The internal limit gauge is made 
in two forms, one as shown in Fig. 62, and which is 
Fig. 62. Pio.63. 




GZ 



CD 



cylindrical, and the other as shown in Fig. 63. These gauges 

are made light and rigid, and are intended for general 

shop use. 

Pio. 64. 



Not Go On 



are made light and 
shop use 

External Limit Gauges.— This 
gauge usually takes the form 
shown in Fig. 64, and is the type 
of gauge intended for general 
shop use. 



Caliper Gauges.— Caliper gauges as illustrated in Figs. 65 
and 66 are frequently used for both roughing and finishing 
work. 

Pio. 65. Fig- 66. 






66 



MEASURING TOOLS AND GAUGES 






Standard Taper Gauges. — The object of using taper gauges 
is for the securing of correct taper holes in machine work and 
corresponding accuracy on the work intended to fit the hole. 
They are in the plug and ring form for external and internal 
work. 

Standard Screw Gauges. — Internal plug screw gauges are 
made from solid bar in the smaller nominal sizes, and in the 
larger sizes from either a solid or shell form blank with a mild 
steel handle forced in or an aluminium handle fitted on ; this 
latter arrangement has the effect of considerably reducing 
weight and bo increasing convenience in use, but it is not 
generally adopted except in the case of the largest sizes. 

Adjustable External Gauges. — This type of gauge generally 
takes the form of a tool with two fixed anvils on one jaw and 
two movable anvils or adjusting screws on the other jaw, 
forming two pairs of measuring faces, the front pair being the 
" go " and the back pair the " not go " points ; the adjusting 
screws are securely locked in position by means of cotters and 
nuts of special design. Each gauge by the length of travel of 
its adjusting screws covers a range of sizes, and can be easily 
and quickly set up to such diameter and limits within its 
range as may be wanted. 

Adjustable Screw Gauges,— Various types of adjustable 
screw gauges are made to suit special requirements. Generally 
the rings are rectangular in form, a cut being made through 
the centre of the screwed part in such a manner that it can be 
adjusted by means of screws, the spring of the metal causing 
it to close in or open out. Screw gauges require special care 
and proper use. 

Position Gauges. — Gauges made from flat cast steel, with 
holes drilled and reamered, which show the position for 
marking off very accurate work. 

Care of Gauges 

The working surfaces of all gauges must always be kept 
perfectly cleaned and oiled. The dropping of a gauge may 
cause it to become inaccurate, and when a gauge has been 
accidentally dropped it should at once be compared with the 
standard gauge, and if necessary corrected. 









Chapter VII 



LATHE WORK AND TURNING 

In order that the lathe hand or turner may be able to 
produce properly finished and accurate work, it is necessary 
that he should be provided with a lathe, accessories, and tools 
that will enable him to meet the following requirements :— 

The lathe must be of suitable size and power. 

Have accessories for doing various classes of work. 

Have lathe tools of correct shape, ground to the proper 
cutting angle. 

The work prepared and set up in a suitable manner. 

The correct speed and feed. 

By fulfilling the above requirements the turner will have 
gone the greater part of the way towards obtaining good 
results. Accuracy in turning comes with practice, and 
cannot be learnt through the medium of a book. 

The Lathe 

The types and designs of lathes are innumerable, special 
repetition work often demanding a special type of lathe. The 
tendency of recent years has been for the larger works to 
provide specially designed lathes for each operation; this is 
particularly so in munition work. The size of a particular 
lathe is generally indicated by a distance taken from the lathe 
centre to the top of the lathe bed, and by the maximum 
distance between the fixed and movable centres. Two other 
important sizes are the amount of swing over the saddle and 
the greatest diameter that can be taken in the gap bed, if the 
lathe is so provided. 

A good lathe should be strong and rigid enough to 
withstand the heaviest cuts without excessive strain, and 
in all cases the bed should have large broad surfaces to 
support the saddle. 



68 



LATHE WORK AND TURNING 



LATHE WORK AND TURNING 



69 



Fig. C7. 



The headstock should be fitted with large bearings, have 
an efficient and well-designed back gear, and be provided with 
a cone pulley to take a wide belt. 

The tailstock or poppet head should be proportionally rigid 
to the fast headstock ; the tailstock spindle should be large, 
ground to size, and provided with an efficient locking gear. 
The screw is best left-handed, and lock nuts should be pro- 
vided at the back of the hand wheel to take up wear between 
the collar and its bearings. An arrangement should be fitted 
by means of which it should be possible to set the tailstock 
centre out of line with the headstock centre, for the purpose 
of turning tapers. 

The saddle or carriage should be provided with large 
bearing surfaces, and should move in the same direction as 
the handles. 

The lead screw, or guide screw, being one of the most 
important parts of the lathe, should be accurately cut, and 
some simple and effective arrangement should be fitted in 
order that the saddle can be connected and disconnected as 
required. 

Some good type of reversing 
action should be fitted. Fig. 67 
illustrates a simple and common 
form of tumbler gear. When the 
lever is down as shown in the 
illustration, then a train of three 
wheels comes into operation, and 
therefore the first and last wheel 
revolve in the same direction. 
When the lever is lifted right up, 
then an even train of wheels comes 
into use and the direction of rotation 
of the lead screw is reversed ; when 
the lever is half-way between right 
up and right down, then neither of 
the wheels gear with the one on 
the lathe mandrel, and therefore no movements take place. 

Surfacing. — For automatic surfacing work, motion is often 
transmitted from t lie lead screw or from a special shaft by 
means of worm wheels and bevel wheels for surfacing work. 

Automatic sliding feed is usually obtained by means of 
special shaft and gearing, but where this is not provided the 
lead screw can be used instead ; to do this, all that is 
necessary, is to put on a compound train of wheels that will 
give a fine thread. 



Driver 




I 






The Countershaft '.—The majority of ordinary lathes are 
driven from a countershaft, which may be arranged to run 
at one or more speeds. The speed of the countershaft is 
determined by the size, power, and required speed of the 
lathe ; it should be fitted with a simple and effective type of 
belt shifting gear. 

The Lathe Back. Gear.— In order to obtain sufficient power 
to take deep cuts on large or heavy work, and also to decrease 
the speed of the lathe, the back gear is used. 

The following is a description of the common type of 
simple back gear : — 

On the lathe mandrel one wheel is keyed called the plate 
wheel, the step-cone pulley and pinion wheel being free to 
revolve if desired. The back shaft has a wheel and pinion 
keyed on to it, and can be drawn into gear either by an 
eccentric motion or by sliding. 

When using the back gear the pulley is free from the plate 
wheel, and the back shaft wheels put into gear. 

When running without the back gear the back shaft wheels 
are taken out of gear, and the pulley is secured to the plate 
wheel by means of a bolt or pin. Thus, when running with 
the back gear the motion is transmitted from the countershaft 
to the cone pulley, which will run free on the lathe spindle 
and drive the hack shaft through the medium of the pinion 
and wheel, this in turn driving the lathe spindle by means of 
the pinion and plate wheel. 

The object of the bank gear being to obtain a large range of 
speeds, and also to take heavy cuts, it is necessary to know 
what the reduction of the speed actually is. 

To take an example. On an 8 in. lathe the speed cone has 
four speeds, the diameter of each speed bring :(£, Bit 6 5> aild 
81 inches. The countershaft pulley revolves at 100 revolu- 
tions per minute. The pinion wheel of the lathe spindle and 
back shaft have 16 teeth each, and the whcols themsolves 
have 48 each. To find the ratio, then 
16 x_16 m 1 
48 x 48 9 
or the back gear will reduce the velocity of the lathe mandrel 
compared with the cone pulley as 1 is to 9, the cone pulley 
revolving nine times as fast as the lathe mandrel. 

The cone pulley having four speeds, by using the back gear 
eight different speeds can be obtained, these being — 



70 



LATHE WORK AND TURNING 

Speed without back gear - - ■ - — - = 224-1. 
3g 



LATHE WORK AND TURNING 



71 



100 x 63 



= 129-2. 



Speed with back gear 



H 

ioo*sft = 77 . 3 

6| 
100x3g =4 , „ 

224 1 






9 
129-2 

9 
77-3 

9 
44-6 

9 



= 24-9. 
= 14-3. 
= 8-5. 
= 4-5. 



The eight speeds obtained being 4-5, 8-5, 14-3, 24-9, 446, 
77-3, 129-2, and 224-1. 



Lathe Accessories 

General lathe work requires the use of quite a number of 
lathe accessories. Fig. 68 illustrates a 12 in. independent jaw 
ehuck, and Fig. 69 shows a two-jaw concentric chuck with 

Fig. 68. Fig. 69. 





slip jaws ; the jaws of this chuck are left blank, so they can 
be shaped to suit the work to be held. Where a variety of 
work is to be turned, then extra jaws can be made to suit the 
particular type of work. 



The /ace plate is a circular cast-iron plate screwed to fit the 
lathe mandrel and then faced and turned on the edge perfectly 
true. Holes and slots are machined or cast m the plate, ana 
it is used in boring and facing operations. The work to be 
bored or faced is screwed to the plate by means of bolts and 

Fig. 70. 




plates. Fig. 70 illustrates a face plate set up for boring 
a three-ilange tee piece. In this example it is necessary to 
use an angle plate; here the angle plate is bolted to the face 
plate and the work secured to the angle plate with a piece or 
iron on the opposite side of the face plate to act as a counter- 
balance weight. . . , 

Stays.— When long slender jobs have to be turned m the 
lathe, unless some support is given to the work, it will spring 
as the tool runs along ; to prevent this springing, stays are 
used. These may be either fixed or moving. 

The fixed stay is chiefly used when turning short and still 
pieces of work. It will also be found convenient for supporting 
jobs requiring internal boring or screwing. 

Generally the fixed stay is applied to some portion of the 
work which has previously been turned ; when this is not 
possible, however, a sleeve can be sometimes fitted on the 
work, and the latter allowed to rotate in the steady. 

The travelling stay or steady is mostly used when the worn 
is parallel nearly its full length. It is secured to the saddle, 
and the chief advantage lies in the fact that support is given 
quite close to the tool. 



72 



LATIIE WORK AND TURNING 



Preparing and Setting-up Work 

All work before it can be successfully turned between 
centres must be first properly prepared by having the ends 
centered. Many methods may be adopted for finding the 
centres, and it depends upon the size and shape of the metal 
as to which is the best method to adopt. For cylindrical 
work the simplest method is to use the vee blocks and the 
scribing block. In other cases it is sometimes simpler to 
make use of the dividers or hermaphrodite calipers, the object 
in the latter case being to strike out four small arcs, each 
being an equal distance from the outside. When the 
approximate centres are obtained a dot is made with the 
centre punch in the centre of the arcs, and the work is then 
tested by being rotated between the centres of the lathe, 
a piece of chalk being held against the metal as it is being 
rotated. If the metal runs out of truth, then the centres must 
be drawn over in the direction required and the job re-tested. 
When the job runs quite true, then the ends are drilled 
up and countersunk. 

For the special purpose of centering work a drill is provided 
which drills and countersinks in one operation. The size of 
the hole depends upon the size and weight of the work ; for 
light work ^ of an inch in diameter or even less, with the 
outer end countersunk 60°. 

In order to transfer the motion from the lathe mandrel to 
the work some form of carrier must be fixed on the work, the 
carrier being driven by means of a pin in the driving plate or 
a bolt in the face plate. 

Setting Work. — The proper order of procedure for turning 
is as follows : Put a little oil on the moving centre of the 
work, and then adjust the tailstock and back centre so that 
the work will revolve quite freely and at Ihe same time not be 
slack, and also leaving it in such a position as to allow the 
saddle and top slide rest to move the required amount. 
Note. — The tailstock spindle should always be as short as 
possible in order to obtain rigidity. 

Procedure. — Select the tool and secure it to the tool holder 
in such a manner that the cutting edge is exactly level with 
the lathe centres. 

Set the lathe to give the correct speed and feed by making 
the necessary adjustments to the belts and gears. 

Try the lathe by giving a few turns on the belt by hand, 
and make quite sure that everything is clear and safe. 

When commencing to turn, if much metal is to be removed, 



LATHE WORK AND TURNING 



78 



start by taking a deep cut. If straight centre work is being 
done, then rough down to within ^a oi an iric, > of ful1 sizc > 
square the ends, and file off any excess of metal at the 
centres, and then re-countersink the holes. 

Replace the work in the lathe and finish to the exact size 
all over. If the work is steel use a plentiful supply of soap 
and water, if cast iron use a broad-nosed tool. 



Speeds and Feeds 

The speed at which a piece of metal should he cut depends 
upon the hardness and shape of the metal, and also upon the 
rigidity of the lathe. It is very difficult to lay down any 
definite rule with regard to speed and feed. So much 
depends upon the job, the strength of the lathe, and the 
quality of the tool steel, that only approximate figures can be 
given. The following table can be taken as representing 
ordinary workshop practice : — 



Metal. 


Cutting Sf>eed. 


Hard steel . . 


. 20-50 feet per minute 


Mild steel . . 


. 35-150 ,, „ 


Wrought iron . 


. 40-120 „ 


Cast iron 


. 35-80 


Brass . . . 


. 60-200 ., 







When taking heavy cuts on hard metal it is preferable to 
decrease the speed and increase the feed ; when finishing on 
wrought iron or mild steel increase the speed and feed ; 
finishing cast iron increase the speed and decrease the 
feed ; when finishing on hard steel retain the speed and 
increase the feed. 

To find Revolutions per minute for a given Cutting Speed 
Multiply the cutting speed in feet by 12, and divide the 
product by the circumference of the work in inches. 

Let R = revolutions per minute, 
cs = cutting speed. 
D = diameter of work. 

„,, _ CS x 12 
Then R = 



74 



LATHE WORK AND TURNING 



Example. — Find the number of revolutions per minute 
a piece of mild steel 3J inches in diameter should revolve at 
in order to cut at the rate of 95 feet per minute. 

Then OTx " x J x8 = 108-6. 
22x7 

Ans. 103-6 revolutions per minute. 

Fig. 70a illustrates a 12 in. belt driven lathe by The American 
Tool Works Co., the swing over the bed is 13.J in. The swing 
over the compound slide rest is 9$ in . The hole in the mandrel 
is 2A in. The size of tool steel used is | x lj in. Width of 
driving belt 4£ in. 

The following is a description of the various parts : — 

Bed construction. — The bed is ribbed transversely with 
heavy double-walled cross girths spaced 2 feet apart. A rib is 
carried lengthwise in the centre of the bed, which has a rack 
cast integral with it. The tailstock is provided with a pawl 
which engages this rack for resisting the end thrust when 
heavy work is being turned. 

The ways of the bed casting are carefully chilled, which 
produces a hard close-grained metal for the V bearings. As 
this provides a harder metal on the shears than on the carriage 
bearings, the wear which takes place will be largely confined 
to the carriage, where it will not impair the accuracy or align- 
ment of the machine. 

The carriage vees are wider and the boa rings longer than are 
usually provided on other makes. The carriage bridge has 
also been widened and is of unusually great depth, due to the 
patented drop vee construction of the lathe bed. 

The compound rest is rigidly designed, the swivel being made 
completely circular and is graduated in degrees. It is clamped 
to the cross slide by means of four bolts. Full-length taper 
gibs, having end screw adjustment are provided on both the 
cross and compound rest slides, these gibs being placed on 
the right-hand side, where they will not receive the thrust oi 
the tool under ordinary working conditions. 

The tailstock is of improved four bolt design, the. rear bolts 
being carried to the top for convenience in clamping. The 
tailstock spindle is clamped in position by means of a double- 
plug binder which is so constructed as to securely clamp the 
spindle at any position without affecting its alignment. 

The lieadstock spindle is made from a special '75% carbon 
crucible steel, and all other shafts, including the lead-screw 
are made of a '45% carbon special ground stock. 



LATHE WORK AND TURNING 



76 




053 



76 



LATHE WORK AND TURNING 



The spindle bearings are equipped with sight feed oil cups, 
and all other important hearings are oiled by means of an 
improved gravity oiling system, the oil being carried to the 
bearings through oil pipes conspicuously located, which hold 
a generous supply of oil. 

A standard thrust bearing is provided which consists of 
alternate bronze and hardened and ground steel collars. The 
bronze collars arc provided with oil grooves. 

Renewable bronze bushed bearings are furnished throughout 
the machine, and the loose gears in the apron are also lined 
with bronze ; the studs on which they run being case-hardened 
and ground, thus providing a hard bearing surface without 
impairing their strength. 

The apron is made in a complete double wall or box section, 
giving all studs and shafts an outboard bearing. The rack 
pinion can be withdrawn from the rack when cutting threads, 
consequently all possibility of chatter or vibration is avoided 
when cutting coarse pitch screws. 

A thread dial is fitted, thus obviating the necessity of using 
a backing belt for thread cutting. The thread dial is placed at 
the right of the apron and can be readily disengaged from the 
lead screw when not in use. 

The lead Hereto is made from 45% carbon ground lead screw 
stock, and is 2 inches in diameter. The maximum variation 
allowed in chasing these screws is '001 inch per lineal foot, and 
they are guaranteed to be within this limit. These screws are 
chased by means of a special lead screw ma-le with a Browne 
and Sharpe master screw. 

The A in. pitch lend scrciv permits engaging the half nuts at 
the proper point when chasing all threads, including those 
having a fractional pitch. This is not only a great time saving 
feature, but is also a safeguard against errors when chasing 
unit threads. 

The coarse pitch lead screw and the comparatively low 
apron ratio required, provides the further great advantage of 
obviating the necessity of speeding up through the quick- 
change gear mechanism for the coarser pilches and feeds. As 
a matter of fact, no member of the quick-change mechanism 
does at any time run faster than the initial driving shaft, and 
the compounding gears are therefore only used for cutting the 
finer threads and feeds. Consequently, a very direct trans- 
mission is provided for heavy turning, etc. 

Steel gearing. — All gears in the entire quick-change gear 
mechanism are regularly made from '45 carbon bar steel. 
The apron gearing is also made of the same material, with the 



LATHE WORK AND TURNING 



77 



exception of two large gears which are made from steel 
castings. 

Tlie cone gears of the quick-change gear mechanism are cut 
with the improved Browne & Sharpe 20 degree involute cutters, 
which form a pointed tooth slightly rounded at the top. This 
is the only proper and satisfactory form of tooth to use in 
a tumbler gear mechanism, as it pennits instantaneous engage- 
ment of the gears without clashing. The pointed tooth also 
has a wider and stronger section than the 14$ degree tooth. 

The tumbler lever of the quick-change mechanism is cast 
steel and is bronze bushed. It is guided into its respective 
positions by means of a slotted plate attached to the front of 
the box. Consequently, the gears cannot be engaged before 
they are in their proper position for meshing. 

The quick-change gear mechanism tortus a complete unit in 
itself and is mounted on the front of the machine, being fixed 
to the bed by means of a tongue and groove which ensures 
permanently accurate alignment. This mechanism is also 
much more accessible for any necessary attention than where 
it is incorporated in the bed under the headstock. It provides 
a range of 48 threads and feeds, all of which are listed on 
a direct reading index plate located above the tumbler lever. 
Provision is made for cutting the following threads: i, |, £, 
I, 1, lft. 1ft, 1|, 1&. 11, 18. 1|. 2. 2ft, 2ft, 21 21, 3, 3£, 3ft, 
4, 44, 5, 5J, 5$, 6, 6J, 7, 8, 9, 10, 11, lift, 12, 13, 14, 16, 18, 
20, 22, 23, 24, 26, 28. 

All compounding in the feed-box is done by means of taper 
jaw clutches, which can be easily engaged. This construction 
is undoubtedly superior to that used on other designs, which 
have a compound mechanism of the tumbler gear type bolted 
on the end of the bed. 

To find Cutting Speed given Revs, per Min. 

— 12— -as. 

Example. — d = 4ft in. K = 50. Find C.S. 

The, * X 4ft X 60 _ 22 X 9 X 50 = 5g . y 



12 



7X2X2 









Chapter VIII 
LATHE TOOLS 

When a lathe is well designed, heavy and very rigid, it 
contributes in itself very much towards its own general 
efficiency as a cutting tool. The value and usefulness of 
a lathe depends almost entirely upon the amount of metal 
it will remove from a piece of work in a given time consistent 
with a finish and accuracy as good and as near as required. 
However, even when a lathe is well designed, successful and 
accurate work can only be done when tools of proper shape, 
having correct cutting edges and proper clearances, are used. 

The fact that the tools being used are all that can be 
desired is not, of course, the only reason for rapid and 
accurate work : speeds, feeds, depth of cut, tool hardness, 
and the quality and nature of the metal being cut, are all 
factors which contribute towards the output and general 
efficiency of the lathe, but whatever the conditions and 
however good they may be, it is only possible to turn out 
satisfactory work when the tools are properly designed and 
correotly ground and fixed. 

Fiq. 71. 



Top Rake- 




ideRake 




'rofi/e Angle. 



When studying the cutting action of lathe tools it is 
necessary to take into consideration the factors which go to 
make up a successful lathe tool. The action of the tool in 
cutting is similar to that of a wedge being driven into a piece of 
work, when obviously the more acute the angle of the wedge 



LATHE TOOLS 



79 



the easier it will penetrate, but only within certain limits, 
because if the wedge is too acute it will be insufficiently 
supported at the cutting edge and will either break off or turn 
over, and if it is obtuse it would be difficult to make it 
penetrate at all. 

Before considering the cutting action of tools further than 
this, it is necessary to be quite clear as to the meaning of the 
different terms used in describing the various angles and 
clearances that can be given to a tool. A common type of 
cranked front tool is shown in Fig. 71. Here the Profile 
Angle is the angle formed by the sides of the nose of the 
tool : the Side Rake is the side slope given to the top of 
the tool ; the Front Clearance is the distance between a line 
at right angles to the body of the tool and the front of the 
tool ; the Cutting Angle, which is perhaps the most 
important factor of all, is formed by the front of the tool and 
the top slope ; and the Top Rake is the amount of slope from 
the cutting point of the tool back towards the body. 

In the case of the wedge it is clear that the more acute the 
angle the easier the wedge will penetrate ; this is true of the 
cutting angle of the lathe tool, but it is obviously necessary 
to support the cutting edge sufficient to prevent it breaking off 
or rapidly wearing away. The tool when in use must go on 
cutting for a considerable time, and therefore it must be well 
supported and backed up at the cutting edge. 

Cutting Angle 

The cutting angle depends first on the hardness and nature 
of the metal being cut, and then upon the amount of metal 
being removed. With cast iron, wrought iron, and steel, the 
harder the material the greater the cutting angle, also the 
heavier the cut the more the cutting edge must be supported 
by increasing the profile angle. For brass and most of the 
bronze alloys the cutting angle requires to be greater than for 
ferrous metal, the top of the tool in most cases being left 
quite flat with the body of the tool. 

With cast iron in particular the metal will be found to vary 
very much ; some will be very soft, some extremely hard. 
The same thing applies to forgings; here the same forging 
may have hard and soft places, and sometimes the metal will 
be extremely hard and dirty on the surface. Gunmetal and 
bronze also range between very soft metal and extremely 
hard metal. 

In spite of the varying nature of the different metals the 
tendency of modern practice is to have the lathe tools ground 



80 



LATHE TOOLS 



by tho tool room department and not by the turner. 
Repetition work, the improvements that have been made 
in the foundry mid .smithy and the advance in the knowledge 
of metallurgy, have made this to a great extent possible. 

While it is not possible to give exact cutting angles for tools 
to be used on the general lathe, the following angles will serve 
as a guide and can be taken as being approximately correct. 



Cutting Angles 



Cast iron 
Brass 



70° 
85° 



Hard steel .... 75° 
Mild steel and wrought iron 65° 

A considerable amount of practical experience will be found 
necessary before it is possible to decide upon the most 
suitable cutting angle and rake for the different classes of 
jobs commonly met with in the repair and general shop. 
The skilled man lias frequently to ulur the cutting angles of 
his lathe tools in order to deal with metal of varying degree 
of hardness and also for such considerations as large diameter 
work, springy work, and work of an intricate character. 

Fbont Clearance 

The question of front clearance is a comparatively simple 
one. Front clearance is the angle formed by the front of the 
tool and a line drawn at a tangent to the work at right angles 
to the centres. For hard ferrous metals the clearance is kept 
as small us possible in order to well support the cutting edge, 
but sufficient to just prevent the front of the tool, below the 
cutting edge, rubbing on the work. For mild steel and 
wrought iron, the clearance is increased in order to obtain a 
more acute cutting angle. This of course is possible because 
the metal being comparatively soft, the tool will stand up to 
the work with less- support than would be necessary with 
a harder metal. 

In the case of non-ferrous metals it will often be found 
possible and desirable to give a greater clearance than with 
either wrought iron or mild steel, and this is due to the 
peculiar nature of the metal. 

The diameter of the work has a considerable influence over 
the front clearance of a tool, and where on a small diameter 
job a tool might have sufficient clearance, on work of large 
diameter the front of the tool would probably rub. 

Side Clearance 

The side clearance of a lathe tool must be considered in 
relation to the feed. The amount given is usually about the 






LATHE TOOLS 



81 



same as for front clearance, but when a coarse feed is being 
used it may be necessary to grind a side clearance to allow 
for the resulting tool advance. This will easily be seen in 
the case of cutting a coarse pitch thread, in which case the 
side clearance must be made to suit the angle formed by the 
side of the thread helix, as shown in Fig. 72. 

Fig. 72. 




Profile Angle 
The profile angle of a tool is more often determined by the 
shape of the work and the character of the cut than by the 
nature of the metal. For front and side tools of the cranked 
type, 60° is generally given, but with other types of front tools 
the profile angle varies to suit not only the particular class 
of machine it is being used upon, but also the various kinds 
of metals being turned. Knife tools, screw-cutting tools, 
parting tools and all tools for special work have profile angles 
to agree with the conditions required. 

Top Rake 

The top rake of a tool is determined by the amount of the 
cutting angle plus the clearance. When turning wrought iron 
or mild steel the metal being removed should be in the form 
of a long shaving, and this can only be accomplished if the 
necessary amount of top rake is given. Insufficient top rake 
will cause the turning to drop off in short chips, and will also 
leave a rough finish on the work, therefore it is important 
that when fibrous metals are being turned as much top rake 
should be given as is consistent with cutting edge support. 

When brass is being turned it is not usual to give any top 
rake, as with the peculiar nature of this metal all the turnings 
will be removed in the form of short chips. 



82 



LATHE TOOLS 




Side Rake 

It is impossible to give any definite angles for either top or side 
rake. So much depends upon the nature of the metal being 
tinned, the amount of feed, and the class of finish required, 
thnt only practical experience and actual experiment can 
determine what is the best allowance in both cases. Top and 
side rake have a great deal to do with the rapid production of 
Rccimito work, and a little practical experience with cutting 
tools will do more to teach the novice what to look for and 
what to avoid than any amount of figures or illustrations. 

If a piece of mild steel is placed in the lathe and a cut is 
taken with a tool, having neither top or side rake, a very poor 
finish will be obtained ; by first giving top and then side rake 
the advantages will be immediately apparent, and if the rakes 
are increased until the cutting edge of the tool wears away 
rapidly the most suitable angles will quickly be arrived at. 

Tool Design 

An example of a crank tool for cutting hard steel is shown 

in Fig. 73. This illustration is not given as being applicable 

to all cases, but is intended to act as a guide and a basis from 

which to start giving top and side rake. Fig. 74 gives the 

Fio. 78. 




J h3' Clearance 



Hard Steel. 
Fro. 74. 




JO'Clcaraace 



Cast Iron. 

approximate cutting and clearing angles for cast iron turning, 
it will be seen that the clearance is increased. Cast iron, 
however, varies so much that in some cases the cutting angle 



LATHE TOOLS 



88 



can be increased to the advantage of the cutting efficiency of 

the tool. a a t 

Cutting and clearing angles for front tools intended lor 
turning wrought iron or mild steel are given in 1-ig. To- 
The cutting angle can in many cases be decreased. Side rake 
is of more consequence here than in the two previous examples, 
and the correct amount can be determined best after a cut or 
two has been taken on the metal itself. 

Fio. 75. 



i ^"Clearance 



Wrought Iron & Mild Steel. 



The example in Fig. 76 can be taken as correct for nearly 
all cases of brass turning. It is seldom necessary to give any 
top or side rake, and a ilat top tool will be found to give a 
good finish and produce accurate work. 




Pio. 76. 



CS3 



< 3^»}r Clearance 



Brass. 



Tool Height 



When tools are set in the lathe tool holder preparatory to 
cutting it is very important that after the tool is placed and 
held down in position that the cutting edge should be exactly 
in line with the lathe centres. This applies in all cases for all 



84 



LATHE TOOLS 



types of tools and all classes of metals. The correct position 
for a tool is shown in Fig. 77. It should be quite flat on the 
holder and dead in line when held down ; the effect of raising 
the tool above the centre will be seen in Fig. 78. Here the 
clearance is decreased, causing the front of the tool to rub on 
the work, and the top rake is increased, making the point of 
the tool weak ami liable to break off; lowering the tool as in 

Fin. 77. 



Correct 
ieightforTopI 

~t h 




Fio. 78. 



/Tool High 
nop-Rake Increased 
'Clearance Decreased 

~$ J - 



Fig. 79 also has a bad effect, as it considerably increases the 
front clearance and at the same time takes away the top rake 
so that instead of the tool cutting as it should do it simply 
grinds away rapidly at the point. 

If the cutting edge of a tool is found to be above the centre 
of the lathe when it is laid on the tool holder, then the tool 
is unsuitable for use in that, lathe ; if on tbe other hand the 
cutting edge is below the centre, it can be packed up to the 




LATHE TOOLS 



85 



correct height without any detriment, provided the packing is 
parallel and extends the full length of the tool and not at 
either of the ends. 

Fig. 79. 



1 



/fool Low , 
NoTopRakl 
Clearance Increased 




?T-i 



dikkction of Feed 

In most cases the feed given to front tools is from the 
tailstock to the fast headstock and the majority of tools have 
their side rake to suit this direction of feed. When, however, 
it is desired to feed with the ordinary front tool from left to 
right, the side rake must be altered accordingly. Such tools 
as knife and side tools have their cutting angles, clearances, 
and side rake ground to suit the altered conditions of cutting. 

Front Tools 
A type of front tool commonly used in repetition work in 
the modern machine shop is shown in Fig. 80. This class of 
Fig. 80. 




Front Cleararce 

Side Clearance 

. , Front Angle 



Side Angle 

tool is very successful when used in conjunction with a rigid 
lathe and when a plentiful supply of cooling liquid is applied 
to the tool nose. 






86 LATHE TOOLS 

Approximate cutting angles for use on various classes of 
metals are given in the table below ; the figures given can be 
modified to suit the various degrees of hardness of metals, 
and also to comply with the different conditions which may 
exist. 



Material. 



Steel, Hard . 
Cast Iron . 
Wrought Iron 
Brass . 



Front 


Side 


Front 


Rake. 


Hake. 


Clearance. 





o 





10 


12 


3 


10 


8 


10 


20 


16 


5 








6 



Side 
Clearance. 



6 

6 
12 



The front and side angles sometimes given to this type of 
tool are shown in Fig. 81. The profile at A will be found to 
stand up well to extremely hard steel when cutting from right 

Re. 81. 




to left; B also is suitable for hard steel and will generally 
give a better finish than A ; for medium hard steels C and D 
will both answer very well, and for soft fibrous metals and 
finishing cuts E gives good results. 



LATHE TOOLS 



87 



Side Tools 

Right and left hand side tools of the cranked type are 
illustrated in Fig. 82. These tools are practically front tools 
bent round to the angle desired. Another type of side tool is 

Fig. 82. 




Fig. 83. 





Riqtib Hand. Left Hand. 



shown in Fig. 83. This tool occupies less room than the 
crank tool, is considerably stiller, and is now more frequently 
used. 



88 



lathe tools 
Knife Tools 



Knife tools for right and left hand cutting are represented 
in Fit,'. 84. These tools are easily forged and can be kept in 
an efficient state without difficulty. They are very useful 
tools, and in many cases can be made to take the place of 
the ordinary front tool. 

Pio. 84. 





Parting Tools 

A parting tool is shown in Fig. 85. Very little top rake is 
given to this tool on account of the tendency for it to dig in. 
The chief point to notice is the side clearance. This should 
be sufficient to prevent rubbing and friction on the metal 
being cut. When turning grooves in chuck or face plate 



Fig. 85. 



Fig. 8(5. 



]=3 




work a larger clearance is given to one side of the tool. The 
amount of this clearance can be found very easily by drawing 
full size circles representing the inner and outer edge of the 
groove as shown in Fig. 86. 

One cut only is taken with the parting tool as a rule, the 
width of the tool cutting edge being slightly smaller than the 
width of the groove. 












lathe tools 89 

Screw-cutting Tools 

Externally V thread screw-cutting tools are generally made 

as shown in Fig. 87. The V is ground to gauge, and 

sufficient side clearance is given to allow the side of the tool 

to clear the edge of the thread helix. 

Fig. 87. 



-€ 



r 

Cfe*ranc»,\_ 



Clearance- 



A solid form of internal screw-cutting tool is shown in 
Fig. 88. The side clearance depends upon the pitch of the 
thread, and the front clearance on the diameter of the hole in 
the work. 



Cheranae 



P 



Fig. 



3> 



Spring Tools 
The spring tool is used to produce a fine finish on work 
which does not require a great degree of accuracy. It takes a 
broad cut or scrape, and very little metal can be used on 
account of its tendency to dig in. It is most useful for 
turning a fillet or a radius on partly finished work. The tool 
is illustrated in Fig. 89, and cutting edges of various shapes 
are shown at A, B, C, and D. 



Fig. 89 





90 



LATHE TOOLS 

Boring Tools 



The most convenient type of boring tool is shown in Fig. 90. 
The tool holder is made from square or oblong section metal 
with the end swayed or turned down us seen in the illustration. 



Fig. 90. 



ffjjj 



3 



-4 






A square section tool is fitted in the square hole at a con- 
venient distance from the end and is secured by means of 
a set screw. 

A solid one piece form of boring tool is shown in Fig. 91. 
The cutting angle and profile of this tool is similar to that of 
the cranked front tool. The front clearance, however, must be 
sufficient to clear the inside of the hole as shown in Fig. 92. 

Pig. 91. 



Fig. 02- 




Clearancs 



Clearance 



Square Thrkad Screw-cutting Tool 

The best form of square thread screw-cutting tool is that 
made from round section steel. The front and side clearances 



LATITE TOOLS 



91 



are normal, the tool being twisted to give the desired amount 
of clearance to suit the angle formed by the thread helix. 
This tool is illustrated in Fig. 93, and the most satisfactory 
method of holding llie s.ime is by means of some form of 



kk;. !i:s. 



a 



Clearance 



Clearance 



Y\c. '.II. 




special holder similar to that shown in Fig. 94. Here the 
tool can be twisted to any angle and without difficulty held in 
position by the dogs of the lathe tool holder. 

Examples of tools used in special capstan machines are 
illustrated in Figs. 95-8. Fig. 95 shows a tool turning a neck 



Fig. 95. 



Fig.! 




92 LATHE TOOLS 

bash, Fig. 96 a round tool for counterboring, Fig. 97 a round 
tool boring a bush, and Fig. 98 a square section front turning 
tool. 



Fig. 91. 



Kin. 




Lathe tools 







Knife Tools 






Parting Tools 


Materials 


Top 
rake 


Side 
rake 


Side 
clearance 


Front 
clearance 


Side Top 
rate rate 


Side 
clearance 


Front 
clearance 


Steel . . 
Cast iron 
Brass 


o 

8 





o 
8 
3 
3 


o 
8 
8 
8 


o 

10 
10 

10 




12 
1 



o 









8 

3 

3 


o 

12 
12 
12 






Lathe Tools 




Side 
Clearanct 



ftgK Left Knife tfong^SZ 
Hand Hand 





Screw-cutting Tools 


Materials 


Top 
rake 


Side 
rake 


Side 
clearance 


Front 
clearance 


Steel . . 
Cast iron 
Brass 


o 
3 
1 




.8 

C 
3 
> 


10 

£ 

> 


o 

12 

12 
12 



Cutting and Cooling Mixtobe 

For turning steel and wrought iron a suitable compound 
can be made by boiling together 10 gallons of water, 1 quart 
of lard oil, 2 lb. of washing soda, and 1 quart of soft soap. 

Cast iron, brass, copper, and babbit metal are usually 
turned dry. Tool steel can be turned dry or with oil. 



Materials 




Front Toole 








Side Tools 




Top 
rake 


Side 
rake 

o 

15 
8 



Side 
clearance 


Front 
clearance 


Top 
rake 


Side 

rake 


Side 
clearance 


Front 
clearance 


Steel . . 
Cast iron 
Brass 




10 
8 



o 
6 
6 
6 


o 

12 
12 
12 


O 

7 
8 




o 

13 
8 



o 
6 
6 
6 


o 

8 
8 
8 






Chapter IX 



SCREW-CUTTING 

Geometrically the screw is the union of a plane cylinder 
having a circular base and a projecting ridge, of uniform shape 
throughout its length, wrapped on the surface of a cylinder in 
a regular spiral. 

Pitch is the distance a nut would travel in one complete 
revolution if the screw had a single thread, or the distance 
between the centre of one thread and the centre of the next, 
measured in a line with its axis. 

Lead is a term used when considering multiple threads, and 
is the distance a nut would travel in one complete revolution, 
or the distance from the centre of one thread to the centre of 
the same thread allowing for one complete turn. 

Inclination of a thread is the angle formed by each of its 
superficial elements of depth, with a plane perpendicular to 
the axis of the screw. This inclination increases in proportion 
as the axis of the screw is approached. The pitch, on the 
contrary, remained constant. 

The Whitworth Thread 

Forms of screw threads vary according to the purpose for 
which they are to be used, and also according to the country 
in which they are manufactured. The form of thread most 
frequently used for general engineering work is probably that 
known as the Whitworth thread. In 1841 Sir Joseph 
Whitworth proposed the adoption of a standard thread for 
bolts, and this system is chiefly used in Great Britain, 
Germany, and the United States. 

Fig. 99. Fig. 100. 

r-*H 



►-£.< 



55 



\d 



-|_n_r? 



The depth of thread is equal to 0'64 of the pitch, the top 
and bottom of the thread is rounded off one-sixth of the depth, 
and the sides form an angle of 55°. 



SCREW-CUTTING 95 

Fig. 99 shows the form of thread— 

The formula being p = pitch = ^ mber threa d 8 per inch 
d = depth = p x 0-6403. 
r = radius = p x 0"1373. 

Square Threads 

The form of the square thread is shown at Fig. 100. 
depth and width is half the pitch. 

Multiple Threads 

Where coarse pitch threads are necessary, in order that the 
thread may be brought within workable size multiple threads 
are used. The difference between a single and double thread is 



Figs. 101 and 102. 



The 




shown in Figs. 101 and 102. Fig. 101 represents a single 
square thread of } inch pitch. Fig. 102 shows a double thread 
of J inch pitch, but having 1 inch lead. 

Calculations for finding Change Wheels 

In nearly all cases the calculations necessary for finding the 
wheels required in cutting a certain thread, is a very simple 
matter indeed. Three things have to be considered ; one the 
pitch of the lathe lead screw, which is a constant and can no 
possibly be altered, the other two are the speed of the job, and 



9G 



SCREW-CUTTING 



the speed of the lead screw. It needs very little consideration 
to see that if you start cutting a thread on a lathe in which the 
work revolved the same number of times per minute as the 
lead screw, then the thread cut will have exactly the same 
pitch as the lead screw. 

A little further consideration will show that if the lead screw 
is made to revolve twice as fast as the work, then a screw will 
be cut having twice the pitch of the lead screw. Also, if the 
lead screw revolves at half the speed of the work, then the 
resulting screw will have a pitch only half that of the lead 
screw. 

The whole question of screw-cutting resolves itself into 
a question of ratio — ratio between the number of revolutions 
made by the job, and the number of revolutions made by the 
lead screw. (See also p. 15.) 



Flo. 103. 



Fig. 104. 




-3 



-3 




-] 



:: 



Before going into the question of finding the ratio, it is first 
necessary to thoroughly understand the names of the wheels 
used in cither a simple or compound train. Taking the simple 
train of wheels first, shown at Fig. 103, here we have three 
wheels, A called the mandrel wheel, C called the lead screw 
wheel, and li the intermediate wheel gearing the two together. 
Ed ihc compound train of wheels, Fig. 104, we have A, mandrel 
wheel, and D, lead screw wlieel, but instead of one intermediate 
wheel, we have two wheels on one stud ; these are called stud 
wheels, the one going on first, D, is called the first stud wheel, 
the one going on second, C, is called the second stud wheel. 



SCREW-CUTTING 



97 



Ratio 

Coming back to the question of ratio, this can always be 
expressed by the following rule : As the number of threads 
per inch of the lead screw is to the number of threads per inch 
of the screw to be cut, so is the number of teeth in the mandrel 
wheel to the number of teeth in the lead screw wheel, or in 
a fractional form : — 

Number of threads per 
inch of lead screw Teeth in mandrel wheel. 



Number of threads per Teeth in lead screw wheel, 
inch of screw to be cut 
It can easily be seen that if the lead screw has, say 4 threads 
per inch, and it is required to cut a screw having 4 threads per 
inch, then the ratio will be as 4 is to 4, or as 1 to 1, in which 
M8<) two change-wheels of equal size would be required, one 
to goon the lathe mandrel, and the other on the lead screw. 
See Fig. 103, with any wheel to gear them together. 

If instead of a 4 thread to the inch screw being wanted, one 
having 8 threads per inch is required, then we get : — 
Pitch of lead screw 4 threads per inch _ 4 teeth in mandrel whee l . 
Pitch of screw to be cut 8 threads - 8 teeth in lead screw 
per inch wheel. 

Fig. 105. Fig. 100. 




= ] 
| 

I 




-] 



-D 



= ] 



Here we see the ratio is 4 to 8, or 1 to 2, that is to say, the 
lead screw is travelling at half ihe speed of the lathe mandrel, 
and consequently a greater number of threads must be cut per 
inch than are on the lead screw. See Fig. 105. 






98 



SCREW-CUTTING 



Taking the example of cutting 2 threads per inch on the 
same lathe, then we get : — 

Pitch of lead screw 4 threads per inch _ 4 teeth in mandrel wheel. 
Pitch of screw to be cut 2 threads 2 teeth in lead screw 
per inch wheel. 

In this case the ratio is as 4 is to 2, or 2 to 1, and the 
lead screw travels at twice the speed of the lathe mandrel. 
See Fig. 106. 

Of course it is impossible to have a wheel with only two 
teeth, but these numbers represent the ratio, and if both 
numbers are multiplied by any other number, then the ratio 
will remain the same, thus the ratio of 4 to 2, is exactly the 
same as 80 to 40 or 40 to 20. 

Change Wheel Examples 

We will now take a few examples : — 

Example 1. — It is required to cut a screw having 4 threads 
per inch, on a lathe with a lead screw having 4 threads per 
inch. Find the necessary wheels. Then : — 

Pitch of lead screw 4 thre ads per inch __ 4 teeth in mandrel wheel . 
Pitch of screw to be cut 4 threads - 4 teeth in lead screw 
per inch wheel. 

The ratio is then 4 to 4, and in order to get the correct 
wheels it is necessary to increase both numbers. As the 
smallest wheel in a set has 20 teeth, we can multiply by 5, 
which gives us 20 and 20. We could also multiply by 10, 15, 
20, or 25 if we had duplicate wheels of those sizes. 

It should be remembered that in all calculations for a simple 
train of wheels, that the size of the intermediate wheel is of 
no importance, and does not effect the question of ratio at all, 
the wheel only being used for the purpose of gearing the 
mandrel wheel to the lead screw wheel. 

Example 2. — It is required to cut a screw having 18 threads 
per inch on a lathe having a lead screw with 4 threads per inch. 

Note. — In all these simple examples it is possible to see at 
once what the ratio actually is, without writing down words or 
figures. In example 2 the ratio is as 4 is to 18, and the only 
thing to do to find the necessary wheels, is to multiply by 5, 
which give us 20 teeth in the mandrel wheel, 90 teeth in the 
lead screw wheel. 

Example 3. — It is required to cut a screw having 9 threads 
per inch on a lathe having 2 threads per inch on the lead 
sorew. 



KCREW-CUTTING 



99 



Here the ratio is as 2 is to 9, and by simply multiplying by 
10, we get the wheels 20 and 90, the 20 being the mandrel 
wheel, and the 90 the lead screw wheel. 

Example 4. — It is required to cut a screw having 1 thread 
per inch on a lathe having a lead screw with 2 threads per inch. 

Here the ratio is as 2 is to 1, so that by multiplying by 20, 
we get 40 and 20, or multiplying by 25, we get 50 and 25 ; 
the former being mandrel wheels, and the latter the lead 
screw wheels. 

Example 5.— It is required to cut a screw having 2 threads 
per inch on a lathe with a lead screw having 6 threads per inch. 

Here the ratio is as 6 is to 2, and by multiplying by 10, we 
get 60 and 20; then mandrel wheel 60, lead screw wheel 20. 

Compound Gears 

The calculations for finding the wheels of a compound gear, 
are exactly the same as for a simple gear. The ratio between 
the thread of the lead screw and the thread of the screw to 
be cut being first found. 

Pig. 107. 




tK 



[" 




Lead Screw 



IttttKtt 



It should be borne in mind that the product of the number 
of teeth in the mandrel wheel and the number of teeth in the 
second stud wheel, is equal to the top figure of the ratio 
fraction ; and the product of the number of teeth in the lead 
screw wheel and the number of teeth in the first stud wheel, 
is equal to the bottom figure of the ratio-fraction. In Fig. 107 
the ratio is as the product of A x A, is to the product of B X B. 

Example 6. — It is required to cut a screw having 4 threads 
per inch, on a lathe with a lead screw having 4 threads per 



100 



SCREW-CUTTING 



inch, the lathe not being supplied with two wheels of the 
same size. 

In this case the ratio is as 1 is to 1, and any two wheels of 
the same size would do in the ordinary course of events, but 
as we have no two wbeels of the same size, it is necessary to 
use a compound gear. To find this gear, we start thus : — 
2x1 

1X2 

by multiplying the first part of the fraction by 20, we can get 
4 x 1 
20 x 2 
and by multiplying the second part by 50 we get 
40 x 50 
20 x 100 
Then 40 mandrel wheel, 50 2nd stud wheel, 20 1st stud 
wheel, 100 lead screw wheel. 

In all cases of compound gear, it is possible to multiply by 
any suitable number, provided you multiply one of the top 
figures by the same number that you use to multiply one of 
the bottom ones. 

Example 7.— It is required to cut a screw having twenty-five 
threads per inch on a lathe having a lead screw with four 
threads per inch . 

Here the ratio i8 as 4 is to 25, and in a simple train of 
wheels it would be necessary to have 20 and 125 wheels. 
As many lathes are not provided with a 125 wheel, it might 
be necessary to have a compound gear. 

To find the wheels for the compound train put down the 
ratio in fractional form and then multiply by 10, thus : 
4 , 10 40 
25 * 10 250 
then make up the compound gear by puoting down two 100 
wheels, thus : 



40 100 
250 * 



100 



cancel to obtain suitable by dividing by 5, thus: 

20 

40 m 

200 X 100 
50 

then we get 40 or 20 mandrel wheel, 20 or 40 2nd stud wheel, 
50 or 100 lead screw wheel, 100 or 50 1st stud wheel. 






SCREW-CUTTING 
Fractional Pitch Threads 



101 



It is common to have to cut threads of fractional pitch, 
thus: 7£ threads per inch, or 1J inch pitch. In all these 
eases the ratio can be found very easily if the following rule is 
carried out. 

Rule. — Find the distance in inches which contain the 
minimum number of complete threads in the screw to be cut, 
and also the number of threads in an equal distance on the 
lead screw. 

Example A. — Find the minimum distance containing 
an equal number of threads on a screw having 7J threads 
per inch. By bringing this number to an improper 
fraction we get '*?, which gives 29 complete threads in 
4 inches. 

Example B. — Find the minimum distance containing 

an equal number of threads on a screw having a pitch of 

1| inch. Bringing this figure to an improper fraction 

gives V, which shows that we have 8 complete threads in 

15 inches. 

Example S. — It is required to cut a screw having 9£ threads 

per inch on a lathe having 4 threads per inch on the lead 

screw. This is best expressed thus : 

£" pitch or 8 threads in 2 inches on 

lead screw mandrel wheel _ 8 

J 1 "pitch, or 19 threads in 2 inches " lead screw wheel ~ *• 
on screw to be cut 

giving a ratio of 8 to 19. Multiplying by five gives us 40 and 
95. Then 40 mandrel wheel, 9"> Lead .screw wheel. 

Example 9.— It is required to cut a screw having 1| inch 
pitch on a lathe having 4 threads per inch on the lead screw, 
then : 

4" pitch or 28 threads in 7 inches 

on lead screw mandrel wheel _ 28 

If pitch or 4 threads in 7 inches lead screw wheel 4 

on screw to be cut 

a ratio of 28 to 4 or 7 to 1. Multiplying by 20 we get 
140 mandrel wheel and 20 lead screw wheel. If a 140 wheel 
is not available then a compound gear must be used ; in that 
case, split the fraction ratio into factors, thus: 

4j^7 

2 x 2 



102 



SCREW-CUTTING 



then multiply each number by 10, which gives : 

40 x 70 

20 x 20 
Multiply the 40 and one of the 20 by 2 gives : 

80 x 70 

20 x 40 

then 80 mandrel wheel, 70 2nd stud wheel, 20 1st stud wheel, 
and 40 lead screw. 

Approximations 

If it is found that the threads of a screw to be cut will not 
factorize with the number of threads per inch on the lead 
screw, then it is necessary to adopt one of two methods. 
By the first method it is necessary to cut a special wheel : 
by the second an approximation is obtained by slightly altering 
the ratio. 

Example 10. — It is required to cut a screw having 67-7 
threads in 12 inches, on a lathe having a 2 thread per inch 
lead screw. The ratio is : 

Lead screw 24 threads in 12 inches 24 

Screw to be cut (57-7 threads in 12 inches 67 • 7 

or a ratio of 24 to 67-7 or 240 to 677. It will be seen that 
the ratio fraction will not factorize, but by adding -3 to the 
bottom number we get the ratio of 240 to 680, and by breaking 
this into factors we can get : 

12 x 2 

17 x 40 
and by multiplying the 12 and 17 by 5 we get : 

60 x 20 

85 x 40 

then 60 mandrel wheel, 20 2nd stud wheel, 85 1st stud 
wheel, 40 lead screw wheel. 

Millimetre Threads 

The cutting of metric threads to approximate sizes is a very 
simple matter. The length of the metre is 39-37 inches, or 
about ijfaj °f an inch less than 39§ inches ; this small difference 
for most practical purposes can be neglected. 

In a length of 39| inches we get exactly 1,000 millimetres, 



SCREW-CUTTING 



103 



and in a length of 39§ x 8 = 315 inches we get 8,000 millimetres, 
and assuming a lead screw with two threads per inch the 
ratio fraction would be 630 to 8,000. If it were necessary to 
cut a screw having a pitch of 1 mm. the ratio would be : 

630 to 8,000, or 63 to 800. 

As 1 mm. is less than the pitch of the lead screw, the 
smallest wheel would be the mandrel wheel, and the largest 
the lead screw wheel. Or to make a compound train, which 
would he necessary in this case, break into factors, thus : 
63 _ 9x7 
800 160 x 5 
Multiplying by 4 we get : 

36 x 7 



160 x 20 
and multiplying by 5 we get : 

36 x 35 
160 x 100 

Then 36 mandrel wheel, 35 2nd stud wheel, 100 1st stud 
wheel, 160 lead screw wheel. 

Example 11. — It is required to cut a thread having a 5 mm. 
pitch on a lathe having £ in. pitch lead screw, then : 

5 



800 80 



x 10 



By adding ciphers to 5 and 10 we get : 
63 x 50 
80 x 100 

That is 50 mandrel wheel, 63 2nd stud wheel, 80 1st stud 
wheel, 100 lead screw wheel. 



Catching Threads 

It will be found in cutting certain threads that the screw- 
cutting tool will not always come in the same position when 
starting to cut the thread ; in other words, the tool will some- 
times cross thread. 

If it were possible to cut a thread with one traverse of the 
tool no difficulty would be experienced by cross-threading, but 
as nearly all screws required several cuts to complete the thread, 
it is necessary to know when a thread can be cut without fear of 
cross-threading, and when not. 



101 



SCREW-CUTTING 



Rule. — When the number of threads per inch on the screw 
to be cut is a multiple of the number of threads per inch on the 
lead screw, then the tool will always pick up the thread in the 
correct place without marking the lathe. 

Example 12. —On a lathe with a lead screw having two 
threads per inch it is possible to cut any even number of 
threads, such as 2, 4, 6, 8, 10, 12, etc., without any fear 
of cross-threading. 

When the threads on the screw being cut are not a multiple 
of the threads per inch on lead screw, then it is necessary to 
take certain precautions. These precautions should be taken 
in the following manner. First, prepare the lathe by setting 
the tool and seeing everything is ready to start cutting, then 
come to the starting position and pull the lathe round until the 
engaging nut of the saddle drops into place ; mark the position 
of the saddle either by bringing the loose headstock up against 
it or by some other convenient menus. Next make a mark on 
the driving plate and a corresponding one on the lead screw ; 
the lathe is then ready for work. Before starting each cut it 
is necessary to come to a position where all the marks agree. 

When cutting short lengths of threads of odd pitch it is 
quicker and safer to leave the engaging nut in position, and 
at the end of each cut pull the lathe back by hand and thus do 
away with the trouble of marking the lathe and the possibility 
of cross-threading. 

Multiple Threads 

The calculations for finding the wheels for cutting multiple 
threads are the same as for single threads, the change wheels 
being found in the same manner, only being based on the fact 
that the mandrel wheel must have such a number of teeth 
that can be divided equally by the number of the separate 
threads to be cut on the screw. Thus, if a three-start thread 
had to be cut, then a mandrel wheel having 30, 45, 60 75, or 
90 teeth would answer the purpose. 

After the correct wheels have been found the method of 
procedure is then : One thread is nearly finished to the 
required depth, the lathe is then brought to the starting 
position. The mandrel wheel is divided into the number of 
parts corresponding with the number of separate threads to be 
cut ; one of these marks must come between two marked 
teeth of the first stud wheel. The swing plate is then lowered 
and the lathe pulled round until the next mark gears with the 
two marked teeth of the stud wheel. The thread is then cut, 



SCREW-CUTTING 



105 



and the operation repeated until all threads are cut, a very 
light finishing cut is then taken along each thread, the tool 
being kept in the same position as regards depth throughout 
the operations. 

Cutting Left-hand Threads 

When the lathe is provided with some form of tumbler 
reverse gear, left-hand threads are cut by simply making the 
necessary alteration to the gear, the required change wheels 
being found in exactly the same manner as for a right-hand 
thread. When the lathe is not provided with a tumbler gear, 
then an extra wheel must be put either between the mandrel 
wheel and the intermediate wheel or between the lead screw 
wheel and the intermediate wheel. In a simple train of 
wheels, as shown in Fig. 108, A is the mandrel wheel, and 
Pig. 108. Fig. 109. 



-] 





zl 



-] 



-3 



D the lead screw wheel, with B and C intermediate wheels: 
the size of B and C are of no consequence, and are only 
intended to gear the mandrel wheel and the lead screw wheol 
together and give the correct direction of rotation. 

Setting Tools for Screw-cutting 

In order to set screw-cutting tools in the correct position 
square with the work, the screw-cutting gauge shown in 
Fig. 109 is generally used. When internal work is being 
screwed it is used as illustrated ; for external screw-cutting the 
small vee in the side is used. 



106 



SCREW-CUTTING 



Table of Change Wheels for Cutting various 
TiTcii Threads 

Lathe Lead Screw t in. Pitch 



Threads to 






Threads 






bo cut 


Drivers. 


Driven. 


to be cut 


Drivers. 


Driven. 


per inch. 






per inch. 








100 


25 


7} 


40 


75 


n 


60 80 


45 30 


8 


40 


80 


IS 


80 


25 


9 


40 


90 


if 


80 120 


110 30 


10 


40 


100 


14 


80 


30 


11 


40 


110 


if 


60 80 


65 30 


12 


40 


120 


if 


80 


35 


13 


20 


65 


ii 


40 80 


50 30 


14 


20 


70 


2I 


40 100 


75 30 


15 


20 


75 


28 


40 100 


95 25 


16 


20 


80 


» 


80 


50 


17 


20 


85 


2g 


40 100 


105 25 


18 


20 


90 


2? 


80 


55 


19 


20 


95 


25 


40 100 


115 25 


20 


20 


100 


B 


80 


60 


21 


20 40 


60 70 


Bi 


HO 


65 


22 


20 


110 


3* 


40 


35 


23 


20 


115 


4 


40 


40 


24 


20 


120 


n 


40 


45 


25 


30 40 


75 100 


5 


40 


50 


26 


20 30 


60 65 


51 


40 


55 


28 


20 30 


40 105 


6 


30 


45 


30 


20 60 


90 100 


6j 


40 


65 


40 


20 55 


100 110 


7 


40 


70 


50 


20 30 


75 100 



SCREW-CUTTING 



107 



Taule of Change Wheels FOB CUTTING various 
Threads 

Lead Screw J in. Pitch 



Threads to 






Tli rends 






be cut 


Drivers. 


Driven. 


to be cut 


Drivers. 


Driven. 


per inch. 






per inch. 






1 


80 


40 


? 


20 


75 


11 


80 


45 


20 


80 


4 


80 


50 


9 


20 


90 


18 


80 


55 


10 


20 


100 


if 


80 


GO 


It 


20 


110 


18 


60 100 


75 65 


12 


20 


120 


n 


80 


70 


13 


20 50 


65 100 


n 


80 


75 


14 


20 75 


100 105 


2 


60 


60 


15 


20 80 


100 120 


n 


40 


u 


16 


25 30 


50 120 


2i 


80 


95 


17 


20 60 


85 120 


84 


40 


50 


18 


25 40 


75 120 


25 


80 


105 


10 


25 40 


95 100 


23 


40 


58 


20 


20 40 


80 100 


21 


40 100 


1 1 1 50 


21 


20 40 


70 120 


8 


40 


60 


38 


20 30 


60 110 


H 


40 


65 


23 


20 50 


100 115 


n 


40 


70 


24 


25 30 


75 120 


4 


30 


60 


25 


20 80 


75 100 


4i 


40 


90 


26 


20 25 


65 100 


5 


80 


75 


88 


20 25 


70 100 


51 


20 


55 


30 


2-1 40 


100 120 


6 


30 


90 


86 


20 30 


100 105 


61 


20 


65 


40 


20 30 


100 120 


7 


20 


70 


50 


20 20 


100 100 






108 



SCREW-CUTTING 



Change Wheels for Cutting Millimetre Pitch 
Lead Screw $ in. Pitch 



Threads to 








Threads 








be nut in 
Milli- 


Drivers. 


Driven. 


to be cut 
in Milli- 


Drivers. 


Driven. 


metres. 








metres. 








1 


36 


Bfi 


160 100 


6 


63 


60 


100 80 


2 


63 


20 


100 80 


7 


63 


70 


100 80 


3 


63 


30 


100 80 


8 


63 


80 


100 80 


4 


63 


40 


100 80 


9 


63 


90 


100 80 


5 


63 


50 


100 80 


10 


63 


100 


100 80 



Proof of Change Wheels 

Divide the number of teeth in driven wheel or the product 
of the teeth in the driven wheels, by the number of teeth in 
the driver or the product of the teeth in the drivers, and 
multiply by the number of threads per inch on the lead screw. 

Finding Lathe Constant 
Place wheels with an equal number of teeth on the first 
driver and lead -screw, and cut a thread. The pitch of this 
thread will be the latho constant. 

Practical Proof of Change Wheels 

After the change gears have been placed on the lathe, drop 
in the lead-screw nut, mark the position of the saddle, and 
pull the lathe a number of complete turns equal to the number 
of threads to be cut per inch. The saddle should then have 
moved exactly one inch. 



SCREW-CUTTING 



109 



Whitworth Standard Screw Bolts and Nuts 



Diameter 
of bolt. 


Threads 
per inch. 


Diameter 

at bottom of 

thread. 


Area at 

bottom of 

thread. 


Hexagonal 

head and nut 

breadth over 

Plats. 


Inches. 


Threads. 


Inches. 


Square inches. 


Inches. 


1 


40 








I 


20 


•186 


0272 


•525 


A 


18 


2414 


0458 


•600 


§ 


16 


•2950 


0683 


710 


A 


14 


•3460 


0940 


•820 


I 


12 


•3933 


1215 


•920 


ft 


12 


•4558 


1632 


1010 




11 


•5086 


•2032 


1100 


1 


10 


•6219 


•3038 


1-300 


I 


9 


'7327 


•4216 


1-480 


l 


8 


•8399 


•5540 


1-670 


1J 


7 


•9420 


"6969 


1-860 


1J 


7 


1067 


•8942 


2 050 


i| 


6 


11616 


10597 


2-220 


i§ 


6 


1-2866 


1-3001 


2410 


if 


5 


13689 


1-4718 


2-580 


If 


5 


1-4939 


1-7528 


2-760 


2 


43 


17154 


23111 


3-150 


2* 


4* 


1-8404 


2'6602 


3-340 


2i 


4 


1-9298 


2-9249 


3550 


2| 


4 


2-0548 


33161 


3750 


% 


4 


2-1798 


3-7318 


3-890 


n 


4 


2-3048 


4-1721 


4 050 


n 


H 


2*3841 


4-4641 


4-180 


3 


H 


26341 


5-4496 


4530 


H 


n 


2-8560 


6-4063 


4-850 


H 


34 


3-1060 


75769 


5180 


3! 


3 


3 3231 


8-6732 


5-550 


4 


3 


35731 


100272 


5950 


4* 


S3 


38046 


113687 


6-380 


« 


n 


4-0546 


12-9118 


6-820 


41 


n 


4-2843 


14-4162 


7-300 



110 



SCREW-CUTTING 



British Association Screws 



For small work. 



Angle of thread 47£ c , rounded at top and 
bottom 



No. 



Diameter 

over ili n 'in I 
(inch). 



Diameter 

at bottom 
of thread 
(inch). 



Threads 

per inch. 






•2360 


•1887 


25-40 


1 


■2090 


•1665 


28' 20 


2 


•1850 


1467 


31-40 


3 


*1610 


•1266 


34 80 


4 


•1420 


•1108 


38-50 


5 


•1260 


"0981 


4300 


6 


•1100 


•0849 


4790 


7 


•0982 


0753 


52-90 


8 


•0860 


0657 


59-10 


9 


•0750 


•0565 


65-10 


10 


•0670 


0504 


72 60 


11 


0590 


•0443 


8190 


12 


•0510 


•0378 


90-90 


13 


•0470 


•0352 


102-00 


14 


•0890 


'0280 


109'90 


15 


•0350 


0250 


120-50 


16 


•0310 


•0220 


133-30 



Bolts and nuts 

Table showing sizes of nuts. Flat to flat = 1^ D + §". 





D = diameter. 




Diameter of 
Bolt. 


Size or Nut. 


Din meter of 
Bolt. 


Size of Nut. 


£ 


r 


H" 


2f" 


I 


w 


if" 

if 


2&" 
2|" 


r 
i" 


w 


1:" 
2" 


2ff 


ir 


r 


2i" 


H" 


H" 


8§" 


3|" 


if 


2ft" 


2J" 


4i" 



Diameter of washers = 2J D. Thickness of washers = £$ D. 
Where D = the diameter of bolt. 



SCREW-CUTTING 



111 



Iron and Steet, Gas, Steam, and Water Tipes 



Nominal Bore. 


Diameter over 
sorewed part. 


Diameter at 
bottom of thread. 


Number of 

threads 

per inch. 


inches. 


indies. 






£ 


•383 


•336 


28 


i 


•518 


•451 


19 


f 


•656 


589 


19 


i 


•825 


•734 


14 


§ 


•902 


•811 


14 


£ 


1041 


•950 


14 


1 


1-309 


1193 


11 


I| 


1650 


1-534 


11 


n 


1-882 


1-756 


11 


if 


2-116 


2-000 


11 


2 


2-347 


2-231 


11 


2i 


2-587 


2-471 


11 


2J 


2-960 


2-844 


11 


2f 


3-210 


3-094 


11 


3 


3460 


3*344 


11 


3* 


3-950 


3834 


11 


4 


4 450 


4334 


11 


45 


4-950 


4-834 


11 


5 


5450 


5 334 


11 


n 


5950 


5 834 


11 


6 


6-450 


6*334 


11 



Chapter X 

DRILLING, TAPPING, AND SCREWING 

Drilling machines are constructed in a very great variety of 
forms. They may be classified under the following heads : — 
Vertical. 
Horizontal. 
Radial. 
Multiple. 
Sensitive. 

In the Vertical Drill, a movable table is usually provided 
for altering the position of the work, and in addition the base 
is planed and fitted with tee-shaped slots in order that the job 
can be, if necessary, bolted down on to it. The larger sizes 
of vertical drills are provided with back gear for giving extra 
power, and also with automatic feeds, and in some cases with 
special arrangements for tapping. 

The Horizontal Drill is chiefly used for work of too great 
a length to be taken in the vertical type of machine. Hori- 
zontal machines are provided with a movable drill-head, and 
in addition to drilling can be adapted for such work as boring, 
tapping, and reaming, 

The Radial Drill is perhaps one of the best types of machine 
for general work. The movable arm can be swivelled to any 
part of the table, and with the universal machine the drill- 
head can be set to any desired angle. Thus any number of 
holes can be drilled in a job without having to move the work 
in any manner whatever after it has once been fixed. 

Multiple Drills or gang drills have two or more drilling 
spindles in the same alignment, or in certain fixed positions. 
The belt-drive is generally taken from a common shaft, the 
speeds and feeds of the drills being variable. A simple type 
of multiple drill is illustrated at Fig. 110. 

Sensitive Drills are constructed with one or more drilling 
spindles as desired. In this type of machine the feed is given 
to the drill by means of a simple lever. 

Drills 

Great improvements have been made in drills within the last 
few years ; the common or flat drill has practically disappeared, 
and its place taken by machine-made fluted drills. 



DRILLING, TAPPING, AND SCREWING 



113 



The twist drill commonly used is made from high-speed 
steel, the fluting and backing off being done in the milling 
machine. A table on p. 114 gives the speeds for various size 
drills. 

Pig. 110. 




Grinding Drills 

The grinding of the cutting edges of twist drills is of such 
importance that special twist drill grinders are provided ; these 
give an efficient and accurate method of grinding drills. The 
cutting edges should have the correct angle, and at the same 
time be uniform with the longitudinal axis of the drill, and 
the lips should be backed off or cleared. If the clearance is 
insufficient or imperfect the drill will not cut correctly, and 
when the feed is put on the probability is that the end of the 
drill will be crushed or split. Drills correctly made and 
ground have their cutting edges straight when at an angle of 
59°. Care must be taken to see that the cutting edges are of 
exactly equal length, as any inequality doubles itself in the work. 



114 



DRILLING, TAPPING, AND SCREWING 



Lubricati(»i 
The use of a good constant flow of cooling mixture to the 
drilling point undoubtedly prolongs the life of the drill, and 
enables the operator to run at a considerably higher speed and 
give an increased feed. For wrought iron and steel, a good 
mixture is made from soft soap, soda, and water. For very 
hard steel turpentine is perhaps the best lubricant. 

Preparing Work for Drilling 
In preparing work for drilling it is usual to first chalk the 
work, and then locate the centre by means of the scribing 

Speeds and Feeds for IIioh-spked Steet, Twist Drills 



Approximate Speeds ami 

Feeds for Wrought Iron and 

Mild Steel. 



Approximate Speeds and 

Feeds for General Cast-iron 

Work. 















Drill 


No. of revs. 


Revs, per 


Drill 


No. of revs. 


Revs, per 


Diameter. 


per min. 


in. of feed. 


Diameter. 


per min. 


in. of feed. 


in. 






in. 






i 


1025 


150 


•i 


1200 


165 


& 


875 


150 


ft 


900 


160 


8 


750 


150 


§ 


865 


160 


i 7 


650 


150 


A 


750 


160 


i 


550 


100 


i 


630 


110 


8 


450 


100 


j 


520 


110 


I 


375 


100 


s 


430 


110 


i 


325 


100 


I 


375 


110 


l 


275 


75 


1 


320 


85 


13 


250 


75 


1J 


290 


85 


4 


225 


75 


1-i 


260 


85 


n 


200 


75 


11 


230 


85 


u 


175 


75 


H 


200 


85 


u 


150 


75 


IS 


175 


85 


2 


135 


75 


2 


155 


85 


2J 


120 


60 


2k 


140 


65 


24 


110 


60 


2J 


12.5 


65 


2§ 


100 


60 


n 


115 


65 


3 


90 


60 


3 


100 


65 


U 


85 


60 


3i 


95 


65 


H 


80 


60 


34 


90 


60 


n 


70 


60 


3* 


80 


60 


4 


60 


60 


4 


70 


60 



DRILLING, TAPPING, AND SCREWING 115 

block, dividers, or some other tool. The centre is marked 
with the centre punch, and from that mark a circle is scribed 
with the dividers, exactly the size of the hole ; inside this 
circle another one is scribed somewhat smaller. These circles 
are dotted with the centre punch, and the work is then set up 
in the machine. Should the drill run out of truth, the 
smaller circle will show how much, and it may be necessary 
to draw it over with a bent round-nosed chisel. 

Screwing by Hand 

Threads are frequently cut by hand by means of the stocks 
and dies ; these are shown in Fig. 111. 

Re. 111. 




The stock is made from one piece of steel, the dies being in 
two parts, and usually fitting in a vee-shaped guide, being 
adjusted or screwed together by means of a set screw. 

In using the stocks and dies, the metal that is to be screwed 
is first turned to the exact diameter of the outside of the 
thread. The dies are placed at the end of the metal and 
slightly tightened ; they are then turned the distance required, 
and turned back. The process is repeated until a full-sized 
thread is cut. 

In using the dies care should be taken to keep the clearance 
spaces free, and when cutting iron or steel to keep the metal 
well lubricated with oil. It should be remembered that dies 
cut in one direction only, therefore they should be only 
tightened up just previous to the cutting movement. 

Screwing Gas Threads 

Stocks and dies for cutting gas threads or tubes are used to 
a far greater extent than the Whitworth dies. With sizes 
below 2 inches it is usual to find a solid, or one piece die 
used; above that size the split form of dies is more often used. 
In either case some form of guide is provided in order to keep 
the thread square with the axis of the tube. 

Previous to using the gas dies it is necessary to grind or file 
the end of the tube slightly tapered, so as to allow the thread 
of the die to get a proper hold of the metal. With the solid 
form of die the thread is cut in one operation. 



Flo. 112. 



116 DRILLING, TAPPING, AND SCREWING 

Cutting Internal Threads by Hand 

Taps are used for the purpose of cutting internal threads. 
Two different systems are in use, the taper and parallel. 

Fig. 112 illustrates a set on 
the taper system. When using 
the taper set of taps, the first 
tap is inserted in the hole 
and carefully turned by means 
of a tap wrench ; when 
the bottom of the hole is 
reached, or the tap lias gone 
through the full length of the 
thread, it is turned back, and 
all the chips of metal blown 
out, and the second tap is 
used. The plug tap finishes 
the thread to exact size. 

With the parallel system 
the same process is gone 
through, the difference being 
that the first tap used is not 
tapered, but simply smaller in 
diameter, and has a shallower 
thread ; the second tap is 
slightly larger, and has a 
deeper thread ; the last tap 
used la of full depth. 




Taper. 



Second. 
Hand Taps. 



Plug. 



To find the correct diameter of a drill for drilling a hole to 
give a full Whitworth thread, multiply the pitch of the screw 
by 1'28, and subtract the product from the outside diameter. 

Example. — To find the size of a drill to cut a hole for 
tapping a 1 in. Whitworth thread. Then — 

Eight threads per inch = £ inch pitch = 0-125. 
0-125 x 1-28 = 0-10. 
10 - 0-16 = 0-84 or? J. 

Size of drill required 2i> the nearest standard size being 
§3 inch. 

Taps for cutting square threads are occasionally made, but 
owing to inaccuracies caused during the hardening process they 
cannot be relied upon. 

A small alteration of pitch in the vee-thread would not be 
noticeable, and if a slight difference were made in the diameter 



DRILLING, TAPPING, AND SCREWING 117 

of the nut and bolt they would screw together; but with the 
square thread, if the pitch is slightly altered, no difference of 
diameter would allow tin- nut to fit. 

To overcome the difiiculties of hardening, it is common 
practice to make the spaces of the tap slightly larger than the 
correct width, but this tap cannot produce a correctly fitting 
nut, as only the first and last thread would be bearing on the 
thread of the nut. 

WniTwoia-H's Staxdaud Taps 



Outside 
Diam- 



% 



:" 

! 

1 
1 
1 
1 

2 



Full 
Length. 



Length 
of 

Screw. 



B 



Length 

of 
Square. 



Size of 
Square. 



Diam- at 

I Bottom 

of 

Thread. 



Threads 

per 

Inch* 



•0418 
•0671 
•093 
•112 
•184 
•1G5 
•136 
•241 
•295 
•346 
-3113 
•456 
•508 
•571 
•622 
•684 
•732 
•795 
•84 
■942 
1067 
1161 

1 286 
1-368 
1-494 
1-59 
1-715 
1-84 
1-98 

2 054 
2-18 
2-304 
2-384 
2-509 
2-634 



BO 

js 

•10 

Bl 

•21 
21 

BO 

18 

it; 
ii 

19 

]:'. 
11 
11 
10 
10 

9 

9 

B 

7 

7 

e 

6 

t, 

6 

•!•; 

4$ 

4 

4 

4 
4 
8 
8 



; 



Chapter XI 

BENCH-WORK 
Vices 

The best type of vice is that with parallel jaws. It is of 
simple construction and can be obtained with hardened steel 
jaws varying between 2" and 5" in width. 

The hand vice is made in a variety of shapes and sizes, and 
is used for gripping objects too small to be held by hand, and 
which require the same manipulation as if held by hand. 

Vice clamps are made from lead, copper, and tin, and are 
used to protect the work from damage by the hardened serrated 
faces of the vice jaws. 

Hammers 

Hammers are shaped to suit the particular work on which 
they are to be used. The engineers' chipping hammer is 
shown at Fig. 113; the usual weight is about li lb. Lead, 

Fig. 113. 




copper, and hide hammers are used in cases where blows have 
to be struck, wit limit braising (ft damaging the metal. 

Chipping. — Hand chipping is now seldom required in the 
modern shop. Before the general introduction of machine 
tools a great amount of work was accomplished by hand, but 
under modern conditions it is not economical to use the hand 
chisel. It is, however, very useful for a workman to be able 
to use the hammer and chisel in a quick and accurate manner, 
as in special circumstances, or when repairs are required in 
out-of-the-way places, this method may be the only one 
possible. 

Chisels 

Chisels are made from crucible steel and vary in length, 
section, and shape according to the particular work for which 
they are required. It is usual to forge chisels from bar steel 
of the same section as that required for the chisel, the ends 









BBNCH-WORK 



119 



being heated and hammered to the shape required. The 
cutting edge is ground on the emery wheel, the angle being 
determined by the metal to be chipped. 

The following may be taken as approximate cutting angles 
for chipping various metals : — 

Cast steel 70°. Wrought iron and mild steel 50°. 
Cast iron 60°. Copper and brass 45°. 

The fiat chisel shown at Fig. 1 14 is used for general chipping 
work and for cutting large surfaces. 



Fia. 114. 



D 



The cross-cut chisel shown at Fig. 115 is used for cutting 
channels on large flat surfaces, or for cutting key way in 
wheels and shafts. 

Fig. 115. 




r 



The side chisel, Fig. 116, is very useful in chipping and 
removing surplus metal in slots and cotter ways. 

Fig. 116. 



The round-nose chisel, Fig. 117, is chiefly used in cutting oil 
channels in bearings and pulley bushes, or for drawing over 
drill centres in drilling. 

Fig. 117. 




120 



BENCH-WORK 
Files 



Files are graded and classified according to their section, 
length, and pitch of teeth. They are forged by hand or power 
from crucible steel, annealed, ground to shape and size, the 
teeth cut, and then hardened by being brought to a cherry-red 
and dipped into salt and water. 

Files vary in length between 3 and 16 inches. The various 
sections of files in general used in the engineers' shop are 
shown at Fig. 118. 

Pig. 118. 
3 F 




CD 



o^ 



a. Hand. 
6. Flat. 

c. Mill. 

d. Square. 

e. Round. 

f. Cottar. 

g. Knife. 
h. Cabinet. 

i. Three-square. 



j. Pit saw. 
k. Half-round. 

/. Cant. 
HI. Crossing. 
n. Cross-cut. 
o. Feather edge. 
p. Diamond. 
q. Tumbler. 



Files are classified according to the spacing of the teeth, 
and are named as follows : — 

Rough. 20 teeth per inch. Second cut. 30 to 40 teeth per inch. 
Bastard. 20 to 25 ,, ,, Smooth. 50to60 ,, „ ,, 

Special ward files and tool-maker's files have from 100 to 
60 teeth per inch. 

Filing 

Considerable skill and a great deal of practice is required 

before the file can be used with any great degree of accuracy, 

and the difficulties of filing correctly can only be overcome 

by constant practice. In using the file the novice should stand 



BENCH-WORK 



121 



directly in front of the work, with the left foot advanced about 
18 inches, holding the end of the file in the palm of the hand, 
with the handle up against the ball of the thumb. When 
using the file take long steady strokes, putting on weight on 
the forward stroke, and relaxing on the backward stroke, at 
the same time keeping the file perfectly horizontal. 

Cross and diagonal filing should be used when lurge surfaces 
are being filed, or when a great amount of metal has to be 
removed. 

When finishing long surfaces, draw filing is frequently done. 
In this method the file is grasped in both hands and drawn 
along the metal in one direction only, and generally parallel 
to the jaws of the vice. This often assists in getting the work 
flat, and brings all the scratches in one direction. 

In using smooth files on soft metals, the teeth will be found 
to pin very quickly, and if the file is not cleaned it will scratch 
the job. Practical experience will overcome this to some 
extent, but the teeth must be cleared by means of a file card. 
A little chalk rubbed on the teeth of the file will help to keep 
the teeth from pinning. 

New files should be kept for filing brass and copper, and 
when the cutting points have worn, the files can be taken for 
the harder metals. 

Scraping 

It is not possible to obtain a perfectly flat surface either by 
means of the file or by machine, and it is often necessary to 
finish work with the aid of the scraper. It is the only method 
by which true surfaces can be obtained, and is applied chiefly 
to the finishing of cast-iron surfaces. 



Fig. 119. 



9>[> 




Scrapers vary in size and shape according to the particular 
work for which they are required. A variety of scrapers are 



122 



BRNCII-WORK 



shown at Fig. 119, these consist of three square, flat, bent 
half-round, and flat half-round. 

In using the scraper a very small amount of metal can be 
removed from any part of the work, and it is thus possible by 
making use of a surface plate to true the surface of any job 
to a fine degree of accuracy. In scraping curved surfaces, the 
three-square or half-round scraper is used, and when a very 
high degree of accuracy is required, the scraping must be 
continued until small transference spots are shown over the 
entire surface. 

Proportions of Keys 
Let D = the diameter of the shaft. 
,, B = the breadth of the key. 
,, T = the mean thickness of the key. 

ThenB= -.- + £"• 

D 

,, T= r + J" for sunk keys. 

" T = To + jJff " for keys on flftt- 

The taper of keys is i" per foot in length, i.e. 1 in 96. 
Steel is the best material for ordinary keys. 

CoLotJBiNQ Solution fob Bright Wobk 

Sulphate of Copper (Saturated Solution) 4 oz. 
Sulphuric Acid . . . . 1 oz. 

Water . . . . • . 8oz. 



C II APT Kit XII 
PLANING AND SHAPING 

The planer is constructed for the purpose of producing plane 
surfaces of larger area than that obtained by means of the 
shapcr. The work to bo operated upon is generally secured to 
a table which moves backwards and forwards, the tool being 
fed at right angles to the work by some suitable gear. 
PLANING am> shaping Tools 



Side Rake Top Rake 




Side_y\ ^ K front Clearance 
Clearance 



□ a 



n rra 





Metal IjS 


Side 
rake 


Front 
clearance 


Side 
clearance 


Front and side tools 
for roughing and 
finishing 


Steel 
Cast iron 


o 

12 
8 


o 

12 
1 


o 

10 
10 


o 
5 
5 


Slotting tools . . . 


— 8 


— 


5 


5 



The older form of planer has two fixed speeds, one for 
cutting and the other for the return stroke. Modern planers 
have a variable speed gear, which allows of a different speed 
being given for cutting different metals. On one particular 
type of machine the cutting speeds can be 30', 40', 50', and 60' 
per minute, with a return speed varying between 90' and 140' 
per minute. 



124 



PLANING AND SHAPING 



For fixing and securing work on the planer the following 
accessories are required: angle plates, parallel packing, levelling 
wedges, holding down plates, hard wood blocks, stopping 
plates, vices, vee blocks, and many special devices. 

Shaping 

The shaper is designed to produce plane surfaces, but of 
smaller area than the planer. It differs from the planer 
inasmuch that the tool moves to give the cut. In some 
examples the work is made to revolve, so that it is possible to 
obtain semicircular work. The return stroke of the shaper is 
unproductive, so it is generally arranged to give the return 
stroke an increased speed. 

The great amount of work done on the shaper can be held 
in the vice, but in the case of large work it can generally be 
bolted to the top or side of the table, or to the base plate of the 
machine. 

A large number of attachments of various kinds can be 
used in conjunction with the shaping machine. The number 
and variety suitable for any particular machine will depend 
upon the class of work it is to bo employed upon. 

The following attachments can usually be obtained for 
application to the modern shaping machine : — 

Parallel, taper, deep jaw, swivelling and round bar vices. 

Revolving, tilting, and swivelling tables. 

Circular motion mandrels. 

Index centres and circidar dividing heads. 

Keyway cutting attachments. 

Concave cutting attachments. 

The cutting speeds of simpers vary between 30 to 50 feet per 
minute. The table on page 109 gives the cutting angles and 
clearances of both planer and shaper tools. 



Chapter XLTI 

MILLING MACHINES AND MILLING 

The universal type of milling machine is probably one of 
the most useful tools to be found in the tool-room of any 
engineering establishment. The wide range of operations, 
and the more general use of this type of machine, makes it 
worthy of careful study by the machine operator. 

A very useful type of heavy universal milling machine is 
shown in Fig. 120. This machine is manufactured by Messrs. 
Brown & Sharpe, and the various parts are as follows : 

The Spindle.— Of crucible steel. Bearings ground. 
Phosphor bronze boxes with means of compensation for wear. 
Front end threaded 4$ in. diameter, 2f , L. H- Has No. 12 
taper hole. Hole through, g in. diameter. Recess in end 
and cap nut for arbor or collet with clutch collar. 

The Drive.— One friction clutch pulley, 18 in- diameter, 
6 in. belt. Runs at constant speed, 320 revolutions per 
minute. Enclosed by belt guard. Back geared. Ratio of 
gearing, 1 to 81*8: L 16 changes of speed, 15 to 350 
revolutions per minute in either direction. Changes made by 
adjustment of index slide and lever. Speeds in geometrical 
progression. _ 

The Arbor Support.— Overhanging arm, solid steel. Both 
bearings clamped from one point. Arm braces, heavy type ; 
provided with phosphor bronze bushing for supporting outer 
end of arbor. Arbor yoke : provided with phosphor bronze 
bushing for supporting arbor at any intermediate point. 
Diameter of holes in bushings, 2 1 " 6 in. An adjustable centre 
provided for use in either arbor yoke or arm braces. Centre 
of spindle to under side of arm, 8g in. Greatest distance, end 
of spindle to centre in arbor yoke, without arm braces, 33 in. 
Greatest distance, end of spindle to bushing in arm braces, 
27$ in. Greatest distance, face of column to arm braces, 
29* in. 

The Table.— Including oil pans and channels, 64$ x 16 in. 
Working surface, 59x16 in. 3 T slots, fin. wide. Quick 
return by internal gear and pinion. Arc of swing, 276°. 
Elevating screw, telescopic. 

Feeds.— Positive. All spur gears driven by chain. Sixteen 
changes varying in practically a geometrical progression, from 



126 



milling Machines and milling 



§ in. to 20 in. per minute. Independent of spindle speeds. 
Range for small mills, -001 8 in. to -057 in. per revolution of 
spindle; for large mills, 041 in. to 1*888 in. per revolution 
of spindle. Au additional series of feeds of less than jj in. per 



Pia. 120. 




minute is provided. No loose change gears. Changes made 
by adjustment of index slide and levers. Automatic feed can 
be used with table set to 48° either side of zero. Hand-wheels 
clutched. 



MILLING MACHINES AND MILLING 



127 



Feed Tripping Mechanism. — Double plunger type. Sensitive. 
Can be set to prevent throwing in of wrong clutch. 

Adjustable Dials.— Graduated to thousandths of an inch. 

Spiral Head and Foot-slock Centres.— Swing 15 in. 
diameter ; take 36 in. length. Hend can be set at any angle 
from 10° below horizontal to 5° beyond perpendicular. 
Graduated to half degrees. Front end of spindle threaded, 
2f in., 4, 11. H. Has No. 12 taper hole. Hole through, 
if in. diameter. Foot-stock centre adjustable in vertical 
plane. Index crank adjustable. Sector graduated. 

Differential Indexing. — Provides for all divisions from 1 to 
382, and many more beyond. 

Vice. — Swivels. Base graduated. Jaws of tool steel, 
hardened. Capacity : l\ in. wide, 2 in. deep, open 4J in. 

Counter-shaft. — Two friction pulleys, 18 in. diameter. 
6 in. belts. Speed, iJ20 revolutions per minute. 

Milling Cutters 

The majority of cutters used on the milling machine have 
the teeth machined from the same material of which the body 
of the cutter is made. Very large cutters, and some specially 
formed cutters, are provided with a means of inserting teeth. 
In using the milling cutter each separate cutting edge acts as 
an ordinary machine tool having a .single cutting edge. The 
cutter when revolving has the work fed to it, and only one 
tooth comes into contact will) the work, and is then only in 
use for a small fraction of time. Thus the wear on the 
cutting edges is uniformly distributed botween the whole of 
the cutting edges, and the intermittent cutting action 
preserves the keenness of the cutting edges. 

Accurate milling can only be accomplished by the use of 
durable and correctly formed cutters, capable of doing a con- 
siderable amount of work without the need for rcgrinding. 

The solid form of plain cutter is a disc of high carbon steel 
made with the front faces of the teeth radial. The angle of 
clearance given, is usually 5°, the laud on top of the tooth 
being left about 0-0:* in. wide. The tooth angle is approxi- 
mately 50°. The side teeth and end teeth being formed 
with a 75° cutter. Cutters of this description vary from 
1 to 4$ inches in diameter, and are made in widths up to 
6 inches. 

Plain milling cutters having straight axial teeth are made 
up to 5 inches in diameter, but the length seldom exceeds 
1 inch. 

The diameter of the cutter detennines to a great degree the 



128 



MILLING MACHINES AND MILLING 



number of teeth. When the teeth are too closely spaced there 
is a tendency for the cuttings to clog in the cutter flutes and 
thereby reduce the cutting efficiency. A number of tests 
with cutters of similar diameter, but having teeth of different 
pitch, have been made, and it was found that by reducing the 
number of teeth 50 per cent the power required was reduced 
about 30 per cent. For roughing work a coarse tooth cutter 
gives a saving in power, is more durable, and allows of a much 
heavier feed than is possible with a closely-spaced cutter. 
Cutters of various types are illustrated in Fig. 121. 

Speeds and Feeds 

The cutting speed is usually taken in feet per minute and 

can be found by multiplying the diameter of the cutter in 

inches by 3-1410, dividing by 12, and multiplying the quotient 

by the number of revolutions per minute of the cutter. 

The following formula will give the number of revolutions 

per minute to be made by a cutter of a given diameter, in 

order to obtain a given cutting speed. 

Let N = number of revolutions per minute. 

,, c.S. = cutting speed. 

,, D ■= diameter of cutter. 

,, if = 8f 

m c.s. x 12 
Then = n. 

x x D 

The feed or movement of the work towards the cutter is 
given as a rule in terms of feet per minute, and may in some 
cases be determined quite independent of the cutting speed. 
A large number of milling machines are constructed in such 
a manner that the feed is entirely dependent upon the speed 
of the machine, and consequently a very coarse feed with 
a very large cutter, or a fine feed with a small cutter, cannot 
be obtained, except within certain limits. This difficulty is 
often overcome by running the feed gear from an independent 
pulley. 

The following rules will give approximate speeds for carbon 
steel cutter on plain straightforward work. With high speed 
steel cutters the speed can be increased up to 50 per cent. 

_ « 200 to 300 No. of revolutions 

For brass Tl — — : — : — r — = 

diam. cutter in inches per minute. 

,, wronght-iron 200 to 250 _ No. of revolutions 

mild steel diam. cutter in inches per minute. 



MILLING MACHINES AND MILLING 129 

Fio. 121. 





Plain Milling Culler With 
Spiral Nicked Teeth 



Shell End Mill with 
Spiral Tee ih 








Side Milling Cutter Metal Stirling Saw 




Two-Lipped Slotting End Mill 



Form Cutter, can be 
sharpened ' without 
changing Contour 
Teeth 



180 



MILLING MACHINES AND MILLING 



For cast iron 

,, annealed 

tool steel 



150 to 200 



diam. cutter in inches 

80 to 100 
diam. cutter in inches 



No. of revolutions 

per minute. 
No. of revolutions 

per minute. 



The Universal Dividing Head 

The universal dividing head, or the spiral head, is used for 
indexing and cutting spirals. The Brown & Sharpe type 
of head is shown in Figs. 122 and 123. This consists of 
a hollow, semi-circular casting in which is mounted a spindle 
connected to an index crank through a worm and worm wheel. 
The worm has a single thread, and the worm wheel has 
40 teeth. 

Pig. 122. 




Indexing 

Indexing with the dividing head is a simple operation 
depending upon the ratio between the number of teeth in the 
worm wheel and the number of threads in the worm. The 
commonest ratio used is 40 to 1, thus every complete turn of 
the crank handle moves the worm wheel a distance equal to the 
advance of one tooth, or fo part of a complete revolution, and 
therefore 40 complete turns of the crank handle would be 
required to turn the bead spindle one complete revolution. 

It follows that to index a piece of work into 40 parts, one 
turn of the crank handle would be required for each division, 
and to index into 80 parts one-half of a turn would be required ; 
also to index into 20 parts two turns of the crank handle would 
be necessary. To find the number of turns or fractions of 



MILLING MACHINES AND MILLING 



181 



a turn the crank handle must be moved for a certain number 
of divisions ; the following rule can be applied : — Divide 40 
by the number of divisions to be made and the quotient will be 
the number of turns or parts of turns to be given to the crank 
handle. 

Applying the Rule 

When the quotient contains a fraction or is a fraction, then 
it will be necessary to give the crank handle a part of a complete 
turn when indexing. 

The numerator of the fraction represents the number of 
holes that should be indexed for each division. If the fraction 
is so small that none of the plates contains the number of 
holes represented by the denominator, both numerator and 
denominator should be multiplied by a common multiplier 
that will give a fraction the denominator of which represents 

Via. 123. 




a number of holes that arc available. If on dividing the 40 by 
the number required the fraction is found to be too large, 
it can be reduced by dividing both the numerator and 
denominator by any suitable common number. For example, 
if seven divisions are required, 40-r7, equals 5$ turns of the 
index handle for each division. As no plate is provided with 
a circle containing 7 holes, this number can be raised by 
multiplying by the common multiplier 8, giving 7 x 3 = 21, and 
if the numerator is also multiplied by 3, then 5x3 = 15. 
Thus for one division of the work, the index crank pin is 



132 



MILLING MACHINES AND MILLING 



placed on the 21 bole circle, aud is given live complete turns 
and then in addition 15 holes on the 21 circle. It would also 
be possible to use the 49 hole circle by taking 35 holes. 

The following tables will be found useful in quickly finding 
the number of turns or parts of a turn to be given to the crank 
handle in order to index all possible numbers up to 360 by the 
plain method. 

Index Table for DBS with Dividing Head. — 1 



Number 


Number of 


Number of 


Number 


Number of 


Number of 


at 


Hole* In the 


Turns of 


of 


Holes In the 


Turn* of 


Division*. 


Index Circle. 


the Crank. 


Divisions. 


Index Circle. 


Ihe Crunk. 


2 


Any 


20 


35 


49 


M'o 


3 


39 


13JJ 


30 


27 


l"A 


4 


Any 


10 


37 


37 


IA 


6 


,, 


8 


38 


19 


1A 


li 


39 


018 


39 


30 


I A 


7 


49 


618 


40 


Any 


l 


8 


Any 





41 


41 


H 


9 


27 


41? 


42 


21 


IV 


10 


Any 


4 


43 


43 


II 


11 


33 


3j{ 


44 


33 


5',' 


12 


39 


345 


48 


27 


H 


13 


39 


sy« 


40 


23 


IV 


! 14 


49 


2J3 


47 


47 


M 


15 


39 


2H 


48 


18 


tl 


10 


2D 


3*o 


49 


49 


H 


17 


17 


2r\ 


60 


20 


18 


18 


27 


2,", 


52 


39 


it 


19 


19 


ft A 


54 


27 


19 


20 


Any 


2 


65 


33 


H 


! 21 


21 


It! 


50 


49 


H 


22 


33 


m 


58 


29 


IK 


23 


23 


m 


110 


39 


II 


24 


39 


IH 


02 


31 


1? 


25 


20 


Mo 


04 


10 


{V 


26 


39 


M4 


05 


39 


H 


27 


27 


m; 


60 


33 


it 


28 


49 


IH 


08 


17 


+T 


29 


29 


M. 


70 


49 


II 


30 


39 


MJ 


72 


27 


M 


31 


31 


• A 


74 


37 


IV 


32 


20 


1A 


75 


15 


TS 


33 


33 


M', 


70 


19 


11 


34 


17 


M'i 


78 


39 


M 



MILLING MACHINES AND MILLING 138 

Index TABES FOB use with Dividing Head. — 2 



Number 


Number of ' 


Number of 


Number 


Number of 


Number of 


of 


Holes In tho 


Tnrw of 


of 


Holes in Uie 


Turns of 


Divisions. 


Index Circle. 


the Crunk. 


Division!. 


Index Circle. 


the flunk 


80 


20 


18 


164 


41 


H 


82 


41 


IS 


165 


33 


IT 


84 


21 


H 


168 


21 


A 


85 


17 


TT 


170 


17 


A 


80 


43 


IV 


172 


43 


IS 


88 


33 


a 


180 


27 


A 


DO 


27 


ii 


184 


23 


A 


92 


23 


is 


185 


37 


M 


M 


•17 


iV . 


188 


47 


18 


95 


19 


a 


190 


19 


T*« 


03 


49 


it 


195 


39 


A 


100 


20 


A 


196 


49 


18 


104 


39 


•1 


200 


20 


A 


105 


21 


A 


205 


41 


j*i 


108 


27 


I? 


210 


21 


ft 


110 


33 


U 


21S 


4T 


A 


116 


23 


A 


216 


27 


A 


116 


29 


H 


220 


33 


,% 


120 


39 


II 


230 


23 


. 


124 


31 


}t 


232 


- 


A 


128 


16 


A 


239 


47 


A 


130 


39 


il 


240 


1R 


A 


132 


33 


:" 


215 


•I!) 


H 


1 38 


27 


5"' 


248 


31 


II 


130 


17 


A 


200 


30 


A 


140 


49 


a 


264 


93 


A 


144 


18 


A 


210 


27 


A 


145 


29 


A 


280 


M 


j'» 


148 


37 


IV 


200 


29 


A 


150 


15 


\: 


296 


37 


A 


152 


19 


* 


300 


15 


ft 


155 


31 


ft 


310 


31 


A 


150 


3!) 


H 


312 


39 


A 


160 


20 


A 


300 


18 


A 



Indexing Degrees 

When it is necessary to divide the circumference of a piece 
of work into degrees, it can be frequently done by plain 
indexing. One complete turn of the index handle produces 
^y of a turn of the work, or %°°» which equals 9 degrees. By 
this method it follows that : — 



134 MILLING MACHINES AND MILLING 

2 holes in the 18 circle = 1 degree. 
2 holes in the 27 circle = jj degree 
1 hole in the 18 circle = § degree. 
1 hole in the 27 circle = | degree. 

Index Sector 

With the Brown and Sharpe dividing head three index 
plates are provided, and contain circles with the following 
numbers of holes : — 

No. 1 Plate— 15, 16, 17, 18, 19, 20. 

No. 2 Plate— 21, 23, 27, 29, 31, 33. 

No. 3 Plate— 37, 39, 41, 43, 47, 49. 

Fig. 124. 




To facilitate the dividing of a given circle of holes the index 
sector shown at A in Fig. 124 is provided. Without the 
graduated index sector, care must be taken in counting the 
number of holes in an index plate when indexing to obtain 
a given number of divisions. The sector enables the correct 
number of holes to be obtained at. each separate indexing with 
little chance of error. The sector consists of two arms which 
may be opened or closed by first slacking out the set screw at 
A, the correct number of holes may be counted, and the sector 
arms set to just enclose' them. 



Chapter XIV 

GEAR CUTTING 
Spur Gears 

Spur gears are toothed wheels which give or receive motion 
from a parallel shaft. They have teeth parallel with the axis 
of the wheel, and when cut in the milling machine generally 
take the form of the involute. 

In connection with the cutting of spur gears the word 
diameter is always understood to mean pitch diameter, and 
pitch diameter is represented by an imaginary circle termed 
the pitch circle which is intermediate between the top and 
bottom of the wheel tooth. The diametral pitch of a spur 
wheel is indicated by the number of complete teeth to each 
inch of pitch diameter. Circular pitch is the distance from 
the centre of one tooth to the centre of the next measured 
along the pitch circle. 

Example : If a wheel has a pitch diameter of 3 inches and 
has 36 teeth, then the diametral pitch is 36-r3, giving 12, and 
for each inch of pitch diameter the wheel has 12 teeth. 

The diametral pitch of a spur wheel being equal to the 
number of teeth to each inch of pitch diameter, it follows 
that each unit will be represented on the pitch circle bj that 
unit multiplied by 3-1416, and the number of teeth to each 
inch of diametral pitch equals the number of teeth to each 
3-1416 inches of circumference. The circular pitch being 
the distance from the centre of one tooth to the centre of the 
next measured on the pitch circle, it follows that the circular 
pitch must be equal to 3-1416 divided by the number of teeth 
in 3-1416 of the circumference, and as the diametral pitch is 
equal to the numbers of teeth in each 3-1416 inches of 
circumference, the circular pitch must be equal to 3-1 116 
divided by the diametral pitch. 

The diametral pitch is obtained from the circular pitch in 
a similar manner to the above; in each 3-1416 inches of 
circumference the wheel will have a certain number of teeth 
which must be the diametral pitch, and being given the 
circular pitch, by dividing 3-1416 by that, we obtain the 
number of teeth for 3-1416 of the circumference which must 
be the diametral pitch of the gear wheel. 



136 



GEAR CUTTING 



W ben it is necessary to obtain the circular pitch, having 
already got the diametral pitch, all that is necessary is to 
divide 3-1416 by the diametral pitch and the result will be the 
circular pitch ; or let P equal the diametral pitch and P 1 the 
circular pitch, then 

8-H16 , 
P 
For example, if the diametral pitch is 6 and the circular 
pitch is required, then 3-1416-=- 6 gives 0-524, which is the 
circular pitch. 

Fig. 125. 



GEAR CUTTING 
Setting Up for cutting Spur Wheels 



187 



The method of setting up a wheel blank is clearly shown in 
Fig. 125. The cutter is placed on the machine arbor central 
with the head and tailstock centre, the wheel blank being 
driven on a suitable mandrel and held in position by means 
of a bent tailed carrier. 

Pig. 126. 





When the circular pitch is given and the diametral pitch is 
required, then we divide 3- 1416 by the circular pitch, or using 
the same formula, 

3-1416 _ 

P 1 

Tooth Relations in Diametral and Circular Pitch 
The rules on pp. 138 and 139 give the formula for obtaining 
the various dimensions required when milling the teeth of 
spur wheels. 



Spiral Milling 

For spiral milling the milling machine is arranged as shown 
in Fig. 126. This operation shows the arrangement for cutting 
teeth in a right-hand spiral cutter. 

The work is 6 inches long and 3 inches in diameter, and an 
angular cutter 3 inches in diameter is employed. An angle of 
11J° is required and the saddle is accordingly set to that angle 
and the head geared to give a lead of 48 inches. 

In considering spirals the distance the helix advances in 
one revolution is termed the lead, and in order to give the 






188 GEAR CUTTING 

DIAMETRAL PITCH. 

Diametral Pitch li the Number of Teeth to Each locli of ibo Pitch Diameter. 



Root. 

Working 

Depth. 

Whole Depth. 

Clearance. 

Clearance. 



Having 



The Circular Pitch. 

The Pitch Diameter 
and the Number of 
Tcetl 

The Outalde Dhimi-. 
tcr and the Number 
of Teeth .... 

The Numberof Tcclh 
and Hie lilaiiK-ir.il 
Pitch 

The Numbci of Teeth 
and 'tuMldo Dlanv 
eter 

The Outaldc Diame- 
ter and ik.- Dl 
etinl Pitch . . 



The Number of Teeth 
and the Dl.-um.-i 
Pitch .... 

The Pitch Din me 
and the Dlnmclral 
Pitch .... 

The Pitch Dlnm 
and the Ku-nbe 
Teeth .... 



Divide 3.1418 by the Circular Pitch 



Divide Number of Teeth by Pitch 
Diameter 



Divide Number of Teeth plua i bv 
OiitBldc Diameter 



Divide Number of Teeth by the 

LH.niK-lr.il Pllcl 

Divide th« product of Outside 
Diameter and Somber of Teeth 
by Number of Teeth plua 2 . 

Subtract from the Outeble Diame- 
ter the quotient of 2 divided by 
the Dlumotral Pilch .... 



Divide Number of Tcclh pint t by 
the Diametral Pltcl 

Add lo the Pitch Diameter the 
nuotlcnt of 2 dlrblcil by tin- 
Diametral Pilch 

Divide the Number of Teeth plua 
■i by the quotient of Nuinlwr of 
Teeth and by the Pitch Diameter 

Multiply the Number of Teeth 
plua 1 by Adduudum . . . 



The Pllrh Dlnmctri 
and il..- Dtamilra 
Pilch 

Tho Outaldc Plame 
terand the Dlamc 
Iral Pitch . . . 

The Diametral Pilch 



The Diametral Pitch. 

The Diametral Pitch. 
Thr Diametral Pllrh. 
The Diametral Pitch. 
The Diametral Pilch, 
ThlckneM of Tonih. 



Divide 1 by the Diimclr.il Pitch, 



hie 1 liy 
or.= £ . 
Divide 1. 1»; by the Diametral Pitch 

DIUde 1 b) the Diametral Pllrh. 

Dl vide J.l&T by the Diametral Pilch 

DliUlc.li: by Ibe Diametral Pllcl 

Divide ThlckneM of Tnoili al 
Bitrh Una i.y hi 



p _ ».uie 



•» 



D'=-£- 



DN 

N+a 



D'= 

D'=D--£- 
D = eN 

D, 



N+a 

E 



D = D'+-£- 
N+» 

" IF 

D = (N+t) I 
N = D P 

N = DP-3 

_ I.-KOS 
P 

.-A 

P 



• t f 
D"= 



DM- f = - 

■-4 



GEAR CUTTING 

CIRCULAR PITCH. 



139 



Circular Pitch la the Distance from the Centre of One Tooth to the Ccnire of the 
Next Tooth, Meaaured along the Pitch Line. 



Having 



Ouulilo 

Diameter 



Root. 

Working 

Depth. 

Whole Depth. 

Clearance. 
Clearance. 



Tbe Diametral Pitch. 

The Pilch Diameter 
and the Nuiiibr 
Teeth .... 

Tho Outaldc Din 
terand thuNumber 
ofTeuth. . . 

The Number of Teeth 
and tho Clrcah 
Pitch 

The Number of Teeth 
and the OuUldcDI 
Bineter .... 

The Outaldc Diame- 
ter and the Circular 
Pilch .... 



The Number of Teeth 
and the llrculu 
Pitch 

Tho Pitch Dlamoicr) 
and u,i- Circular 
Pilch 



Tho Pitch Plaiiirtir 
and tho Circular 
Pitch .... 



The Circular Pilch. 
The Circular Pitch. 

The Circular Pitch. 

The Circular Pilch. 

The Circular Pitch. 
The Circular Pitch. 
ThlckneM of Tooth. 



Divide 8.1418 by loo Diametral 
Pilch 

Divide Pitch Dlnmeter by ihe 

Srodiicl of .81ns mid Number of 
uoth 

Divide Outaldo Diameter by ihe 
product of .3183 and Number of 
Teeth plua t 

The continued product of ihe 
Number of Teeth, the Circular 
Pitch und .:u.-:i 

Divide the product of Number of 
Teeth ami Otiuldc Diameter by 
Number of Teotb pluaS . . . 

Subtract from Ihe Outaldc Diamc 
tcr the proiluct of tho Circular 
Pitch and .8386 

Multiply Ihe Number of -Teeth by 
the Addendum 

The continued product of the 
Number of Tccih plus *, the 
Circular Pilch aud J ls3 . . 

Add to the Pitch Diameter the 
proiluct of tha Circular Pilch 

and aas 

Multiply Addendum by Numlier 
of Tcclh plll»-i 

Divide the product of Pilch Dlam 
eier nnd 8.14111 by lbs Clrcubi 
Pitch 

One half the Circular Pllrh . . 

Multiply the Circular Pilch by 
.31S3, or» = ^.' 

Multiply the ClrriiUr Pitch by 

Multiply the Clrculnr PIU-h by 

Multiply the Circular Pilch by 
.0888 

Multiply the Circular Pitch by M 

Onetcnth the Thlckncaa o* Tooth 
at Pitch Line 



p,_ 3.1418 



!••■= 



.3itaN 



.3183 N+J 
D^NP\3183 



ND 

N+3 



D-=-i^r 



D = D— (PMS366) 
D'=Ne 

D=(N+S)P'.SJa 
D=D'-KP'.8S8«) 

D = a(N+5) 

D' 3.1418 
•> - r , 

• = P-J1«S 

• + 1 = P' JM 
D"= P .1368 

D"=r.r«,6 

t = P .05 

f=4- 



140 



GEAR CUTTING 






necessary rotation to the work the spiral head is used. The 
feed screw of the machine generally has 4 threads per inch, 
and the spiral head is usually geared so that forty turns of the 
worm are required in order to make one complete turn of 
the spiral head spindle, and therefore if a train of change 
wheels are used which give a ratio of 1 to 1 then the spiral 
head will move a complete turn when the table has travelled 
a distance of 10 inches, and the work will have a lead of 
10 inches. 

The various wheels used are named : Gear on Worm, 
Second Stud Wheel, First Stud Wheel, and Gear on Screw. 
The wheel on the table screw and the first stud wheel are 
drivers, and the wheel on the worm and the second stud 
wheel are driven. The wheel arrangement is clearly shown 
in Fig. 127. 

Pig. 127. 




fto Gem Om Stud 



By taking advantage of the various combinations of wheels 
the ratio of the longitudinal movement of the table to the 
spiral movement of the work can be altered to suit nearly all 
requirements. 

A table for finding the approximate angle and necessary 
wheels for cutting spirals will be found on pp. 142-4. This 
table is suitable for all Brown & Sharpe machines and for other 
machines geared in a similar manner. 



GEAR CUTTING 



141 



Calculations for Change Wlieels 
The calculations necessary to find the required change 
wheels to give a desired spiral are practically the same as for 
finding lathe change wheels for screw cutting. In lathe work 
the ratio of the driving and driven wheels is the ratio between 
the number of threads to be cut per inch and the number of 
threads per inch on the lead screw. On the milling machine 
the ratio of the driving and driven wheels is the ratio of the 
lead of the spiral to be cut and the lead of the machine table ; 
or the compound ratio of the driven to the driving wheels 
equals the lead of the required spiral to the lead of the 
machine table. 

This expressed in fractional form would be — 

Lead of the requ ired spiral _ Driven gear 
Lead of machine table Driving gear 
and if the lead of the machine is 10 inches, then 

Product of driven gear lead of the required spiral 
Product of driving gear 10 

or ten times the product of the driven wheels divided by the 
product of the driven will give the lead of the resulting 
spiral in one complete turn. 

Ratio 

If the required spiral has a lead of 14 inches the ratio will 
be as 14 is to 10, or, dividing the lead by 10, the quotient 1-4 
will be the ratio to 1. 

If the required spiral has a lead of 36 inches the ratio will 
be as 36 is to 10, or dividing 36 by 10, we get the ratio of 
3-6 to 1. 

Examples of Change Gears 

Example. — Find the necessary gears to cut a spiral having 

a lead of 27 inches. 

The ratio is as 27 is to 10, and can be expressed as 

27 
a fraction thus, — ; this fraction can be broken into factors 

3 9 

giving-^- x -- Taking each fraction separately and multiplying 

the numerators and denominators by 16 and 8 respectively, 

3 16 48 ,9 8 72 
Weget 2 X r6 = 32 and 5 X 8 = 4V 

Then 32 and 40 are driving gears, and 48 and 72 driven 
gears. 



142 



OEAR CUTTING 



I: 



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8. 

x ; 

5- 



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if 



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on o'on'o JS9SS * r^o«in"* ANXNioeiS 



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m 0-*i 995«eQ»l-tiOioneO")N-i»l>N- 

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GEAR CUTTING 



143 













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144 



GEAR CUTTING 



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GEAR CUTTING 



145 



Table Angle for Cutting Spirals 
After the necessary change wheels to cut the given spiral 
have been placed in position, it is necessary to find the correct 
angle the table must be set to in order that the cutter will be 
correctly in line with the helix. 

The spiral angle depends upon the circumference of the 
work and the lead of the spiral. The greater the lead of the 
spiral of any given diameter, the smaller the angle ; and 
the greater the diameter of the spiral with a given lead, the 
greater the spiral angle. It will be seen that if the circum- 
ference is increased or decreased and the lead remains the 
same, there will bo a corresponding change in the angle, and 
for that reason the circumference is not always taken when 
calculating the spiral angle. The correct angle should be 
Fio.128. 




found, not by the outside diameter of the work, but from the 
pitch diameter. 

If the required angle cannot be found in the tables on 
pp. 142-4, then two methods are available. 

The spiral angle can be found by first obtaining the natural 
tangent of the angle by dividing the circumference by the lead 
of the spiral, and when the tangent is known the corresponding 
angle in degrees can be found from a table of tangents. In 
formula this would be : — 

Let C = circumference in inches. 
,, I, = lead in inches. 
,, T = tangent. 

Then T = -- or L = - 

L T 



146 



GEAR CUTTING 






Example. — If the pitch diameter is 3£ in. and the lead of 
the spiral 24 inches. Find the angle. 

Then c = 3J x w = 10-21. 
„ T = 10-21 -f 24 = -425. 

From a table of tangents -425 gives an angle of 23 ft. 10 in. 

The other method of determining the angle of the spiral is 
a graphical one. In Fig. 128 AB is equal to the pitch circum- 
ference and AC the lead, then bc is the required angle which 
can be taken by means of a protractor. 



Diametral Pitch, Circular Pitch, and Addendum. 










Approximate 


Diametral 


Circular 


Full Depth 


Addendum. 


or nenrest 


Pitch. 


Pitch. 


of Teeth. 


Circular 










Pitch. 


1 


31416 


21571 


10000 


3" 


li 


2-5133 


1-7257 


•8000 


2i" 


H 


2-0944 


1-4381 


•6666 


2" 


n 


1-7952 


1-2326 


•5714 


If 


2 


1-5708 


1-0785 


•5000 


ir 


2i 


1-3963 


•9587 


•4444 


if 


9$ 


1-2566 


•8628 


•4000 


ir 


3 i 


1-1424 


•7844 


•3636 


J,f 


3 


10472 


•7190 


•3333 


3J 


•8976 


•6163 


•2857 


i" 


4 


•7854 


-5393 


•2500 


r 


5 


•6283 


•4314 


•2000 


r 


6 


•5236 


•3595 


•1666 


r 


7 


•4488 


•3081 


•1429 


r" 


8 


•3927 


•2698 


•1250 



Chapter XV 

PRECISION GRINDING 

The very great improvements made in grinding machines 
and grinding wheels in recent years has led to the almost 
universal use of grinding as a means of producing precision 
work. 

The grinding machine is not only used for finishing work 
to very 6ne limits, but it also, in many cases, shows to 
advantage in producing work from the rough. 

It is due to the very accurate feeding arrangements, and 
the simple means by which work can be reduced to a pre- 
determined size, that the grinding machine is particularly 
useful and economical on repetition work. The same features, 
however, which make the machine advantageous on repetition 
work can be applied to a single article, because, after taking 
a few trial cuts over the work, the amounts oversize can be 
removed with great exactness by means of the automatic 
feeding arrangements. 

The development of grinding machines will be appreciated 
when it is mentioned that the Churchill Machine Tool Co., 
Manchester, are manufacturing machines having a swing of 
50 inches, and admitting 25 feet between centres. This 
machine weighs 45 tons, and is provided with a grinding 
wheel of 50 inches diameter and 5 iuch face. It is driven by 
means of two electric motors, a constant speed motor of 
45 horse-power driving the grinding wheel and feeding gears, 
while a variable speed motor of 15 horse-power drives the 
work. 

Erecting Grinding Machines 

When grinding machines are being erected the instructions 
of the makers should be strictly carried out, and particular 
attention should be given to the question of speeds. Unless 
the speeds and feeds are correct, and the machine is rigid 
and level in all directions, successful and accurate work will 
not be possible. 

Abrasive Materials 

Emery is an intimate mixture of corundum (oxide of alumina) 
and magentite (oxide of iron). It is found in Eastern Europe, 
Asia Minor, and North America. Corundum which gives the 
emery its hardness is found in two forms : sapphire, which 
is transparent, and commercial corundum, which is translucent 
but not transparent. 



148 



PRECISION GRINDING 



Emery contains a considerable percentage of impurities 
which have a tendency to burn instead of cut, and it is on 
that account the emery wheel is so inferior to the corundum 
wheel. 

Artificial Abrasives 

Many artificial abrasives are now used in place of emery, 
and are known under such names as aloxite, alundum, boro- 
carbon, carborundum, corundite, crystolon, eleclrite, etc. ; 
these are produced either by fusing bauxite or some other 
material with a high alumina content ; or by fusing sand, 
coke, sawdust, and salt in an electric furnace at a temperature 
of about 4,000° Fah. 

Production of Grinding Wheels 
Grinding wheels are produced by at least four distinct 
methods : — 

(1) Vitrified Wheels are manufactured by mixing the 
particles of grits with a bonding clay of suitable consistency ; 
after mixing the material is run into moulds and allowed to 
partly dry ; the unfinished wheels are then shaped to size, 
and ag8in dried. They are finally placed in a kiln and are 
subjected to a temperature at which the clay vitrifies; a 
process requiring from 5 to 20 days according to size. 

(2) Silicate Wheels are produced by mixing the grits with 
a bond, of which silicate of soda is the principal ingredient ; 
the temperature of the kiln for this process is lower than 
required with the vitrified process. 

(3) Elastic Wheels have their grits moulded with shellac as 
the principal ingredient of the bond ; they are baked at a 
temperature sufficient to set the shellac. Elastic wheels are 
sometimes produced with vulcanized rubber as the bond 
for the grits. 

Grade and Grain 

Grade. — The term grade is used when referring to the 
hardness or bond of the wheel, or the resistance of the grits 
to disintegrate when under cutting pressure. When the 
grit particles can be easily broken away from the bond, 
the wheel is termed soft, and when the wheel retains its 
particles longer it is termed hard. 

The grades between very soft and extremely hard are 
obtained by varying the amount of bond, the harder the wheel 
the greater the amount of bond and the smaller the amount 
of grits. 

An ideal wheel is one in which the grit particles break 
away from the wheel as soon aB they become dull. 



PRECISION GRINDING 



149 



The various degrees of hardness are designated by means 
of the letters of the alphabet, A being extremely soft and 
Z extremely hard, M being medium. The wheels in general 
use vary from G to R, but J to M will be found to cover the 
greater part of the work met with in the engineering workshop. 

Grain 

The size of the abrasive grit particles used in the 
manufacture of the wheel indicates the degree of its fineness 
or coarseness, and is termed the Grain. 

The abrasive material, after being crushed, is sifted and 
graded according to size. The numbers used for vitrified 
wheels are determined by the size of the mesh of the sieve. 
For example, grit number 30 indicates grits which have 
passed through a sieve with 30 meshes to the linear inch. 

The degree of coarseness varies from about 8 to 200, but 
grit numbers 16 to 60 will cover most general engineering 
work. 

The following table shows the method of indicating the 
hardness of the different types of wheels : — 

Table Showing Degrees of Hardness of Grinding 
Wheels. 



Degrees 


Vitrified 


Silicate 


Elastic 


of Hardness. 


Process. 


Process. 


Process. 


Soft . 


E 
F 








G 


G or J 


i E 




H 


H „ i 


| E 


Medium Soft 


I 


I » 1 


1 E 




J 


J „ 14 


HE 




K 


K „ 2 


2 E 




L 


L „ 2J 


2J E 


Medium . 


M 


M „ 3 


3 E 




N 


N „ 3J 


H B 







„ 4 


4 E 




P 


P „ H 


4£ E 


Medium Hard . 


Q 


Q „ 5 


5 E 




B 


R „ 6 


8 E 




S 


S „ 7 


7 E 




T 






Hard 


u 







150 



PRECISION GRINDING 






With the silicate wheel the degree of hardness is indicated 
by some manufacturers by letters and some by figures. 
When letters are used they correspond to the letters used in 
referring to the vitrified wheels. 

Use of the Grinding Wheel 
Before the grinding of a piece of metal is actually com- 
menced, the following factors have to be considered : (1) The 
grade and grain of the grinding wheel. (2) Speed of the 
grinding wheel. (3) Speed of the work. (4) Feed of the 
work. (5) Depth of cut. (6) Water supply to the work. 

Selection oe Wheel 

(1) Of the above factors the most difficult to determine is 
probably the first. Most manufacturers will furnish users 
of wheels with a list showing the most suitable grain and 
grade for various classes of grinding. This, together with 
some practical experience, will soon enable the user to select 
the correct class of wheel for most purposes. A list of grinding 
wheels showing the grade and grain for different materials 
is given on p. 162. 

If on using a wheel it is found to glaze quickly a softer wheel 
should be tried. Should the work become overheated, and 
the wheel does not glaze, the overheating can often be reduced 
by increasing the work speed; should no improvement result 
a softer wheel should be tried. 

When the wheel wears excessively, reduce the speed of the 
work ; if the wheel still wears, try a harder grade wheel. 

Increase of diameter of the work increases the arc of 
oontact, and a wheel working satisfactorily and efficiently on 
a piece of work of small diameter may not be efficient on 
a similar materia] of larger diameter ; in this case a grade 
softer wheel should be tried. 

Speed of Grinding Wheel 

(2) The peripheral speed of the grinding wheel is usually 
between 5,500 to 6,000 feet per minute. In all cases the speed 
given by the wheel manufacturers should be strictly adhered to. 

-Speed of Work 

(3) Work speeds depend upon many factors and range 
between 25 and 60 feet per minute for external cylindrical 
work, and between 100 and 120 feet per minute for internal 
work. The low speed generally for work of large diameter 
and the higher speed for work of smaller diameter. Too low 
a speed has a tendency to cause local overheating, and 
too high a speed will often cause vibration. When the 






PRECISION GRINDING 



151 



wheel glazes quickly an increase of work speed can be tried, 
while if it wears rapidly a decrease in work speed may improve 
matters. 

Feed of Work 

(4) The width of the wheel to a great extent determines 
the amount of table travel. For roughing a transverse 
movement equal to two-thirds of the wheel width can be 
given per revolution of the work. For finishing the movement 
should be reduced to half the wheel width or less if necessary. 

Depth of Cut 

(5) When rough grinding work on which the turning marks 
are distinctly showing, a maximum cut of "006 can be taken 
at each end of the table traverse. When the tool maris are 
ground out, the cut should be reduced to -0015 to - 002, and 
when taking the last few cuts for finishing, the depth of 
cut should be reduced to -00025 to -0005. 

Water Supply 

(6) The full available water supply should be used in all 
grinding operations. The water stream should be directed 
on to the position where the wheel makes contact with the 
work. 

A very suitable grinding liquid is a solution of 2$ gallons 
of water, 3 lb. of soda, and J pint of soluble cutting oil, and 
is much better than plain water. 

Shape of Wheel Faces 
The following diagram shows some of the wheel faces in 
general use. The round and bevel faced wheels are chiefly 
used for sharpening saws. 




152 



PRECISION GRINDING 



Grade and Grain of Grinding Wheels for Different Materials' 



(The Norton Co.) 



Class of Work 



Aluminum castings 

Brass or bronze castings f large! . , . 
Brass or bronze castings (small). . . 

Car wheels, cast iron 

Car wheels, chilled 

Cast iron, cylindrical 

Cast iron, surfacing 

Cast-iron (small) castings 

Cast iron (largel castings 

Chilled iron castings 

Dies, chilled iron 

Dies, steel ■, 

Drop-forgings 

Internal cylinder grinding 

Internal grinding, hardened Steel. . 

Machine shop use. general 

Malleable iron castings (large). . . 
Malleable iron castings (small) . . . 
Milling cutters, machine grinding 

Milling cutters, hand grinding 

Nickel castings 

Pulleys, surfacing cast Iron 

Reamers, taps, etc.. hand grinding. . 

Reamers, taps, special machines 

Rolls (cast iron), wet 

Rolls (chilled iron), finishing 



Grain Grade 



20 
24 comb. 
20 to 46 
24 to 30 
16 to 20 
20 to 30 



Rolls (chilled iron), roughing. ...... 

Rubber 

Saws, gumming and sharpening. . . 

Saws, cold cutting-oft* 

Steel (soft!, cylindrical grinding. . J 

Steel (soft), surface grinding 

Steel (hardened). cylindrical grind- ( 

ing I 

Steel (hardened), surface grinding. 

Steel, large castings 

Steel, small castings 

Steel (manganese), safe work 

Structural steel 

Twist drills, hand grinding 

Twist drills, special machines 

Wrought iron 

Woodworking tools 



36 to 60 
20 to 30 

46to60 
20 to 36 
14 to 20 

20 to 30 

46 to 60 

■1>. io GO 
20 to 24 

46to60 

46 to 60 

24 10 36 

70 



M to 50 

36 to 50 

60 

24 comb. 
46 to 60 
24 to 36 

24 comb. 
I6to60 
36 to 46 
12 to 20 
20 to 30 
16 to 46 
16 to 24 
46 to 60 
36 to 60 
12 to 30 
46 to 60 



3 to 4 
Elas. 



Q 

JtoK 
HtoK 
PtoR 

PtoR 
toU 



JtoL 
PtoR 

jtoM 
OtoQ 
PtoU 
PtoR 
H to M 
JtoM 
PtoQ 

Kto'6 
JtoM 
JtoM 

mto2 

Elas. 



JtoK 
MtoN 
OtoQ 
LtoN 
LtoN 
HtoK 

K 
JtoL 
HtoK 
QtoU 
PtoR 
LtoP 
PtoR 
" M 
KtoM 
PtoU 
K to M 



Cryatolon 



20 to 24 

20 to 24 
24 to 36 
16 to 24 
16 to 24 
30 to 46 
16 to 30 
20 to 30 
16 to 24 
20 to 30 
20 to 30 



16 to 20 

■0 to 3H 



20 to 24 
30 to 36 



24 to 36 
70 to 80 



30 to 46 
30 to 50 



PtoJc 

QtoR 
PtoR 
PtoR 
OtoQ 
JtoL 
ItoL 
QtoS 
QtoS 

Q 
OtoQ 



R toS 
QtoS 



R 

KtoL 



JtoM 

IV, to 2 

Elas. 

2 to 3 Elas. 

KtoM 



• The information contained in this table is general and only intended to give 
i approximate idea of the grade used under ordinary conditions? 



precision grinding 
Wheel Turning 



153 



An unglazcd wheel should only require burning when a fine 
finish is required, and one turning of the wheel should keep 
it in good cutting condition for at least half an hour. 

For turning wheels a diamond should be used, and this 
should be held in a special bolder and fixed in a rigid 
position. 

In turning the wheel a number of very light cuts (-0005) 
should be taken, using a fine traverse, and the maximum 
amount of water. 

Chattering 

An improperly fixed machine or lack of rigidity is a frequent 
cause of chattering. When the wheel is running out of 
truth or is badly balanced, or if the work is rotating too 
fast, there is a possibility that chatter marks will result. 

Chatter marks on a long slender job can be overcome by 
the use of suitable steadies. 

Travel of Work 

When grinding internal or external cylindrical work, fehe 
traverse of the table should not allow the work to be carried 
completely away from the stone ; not more than one-third 
the width of the stone should project beyond the ends of the 
work at each end of the stroke. 

Grinding Allowance 

The amount of metal to be left on the work for grinding 
depends to a large extent upon the size and power of the 
machine being used. Generally anything above ^j inch is 
more economically removed in the lathe or other machine by 
turning. 

In all cases sufficient metal must be left to clean up all 
over, but time should not be wasted in turning metal to too 
fine a limit. On hardened steel cylindrical work about 0-02 
will be found sufficient, while on unburdened work 001 to 
0-015 will be satisfactory. For internal grinding the grinding 
allowances vary from about 0'008 to 0-015. 



Chapter XVI 

TAPERS AND TAPER TURNING 

When the terms " taper per inch " or " taper per foot " 
are used, it means that in one inch or one foot there is a 
difference between the smaller diameter and the larger 
diameter of a given amount. In Fig. 129 the taper is J in. 
per inch, and in Fig. 130 the taper is i in. per foot. 



Fig. 130. 
SL 




TM>£0j£p£S> FOOT 



IfiPBu'^PenlNCH. 



Fi<;. 131. 



% 



1f*c# fU' in £& Inches. 



In some cases the length of the taper is given in inches 
and fractions of an inch, as in Fig. 131 ; here the taper is 
\ in. in 2 J inches.Vhich is equal to J 4- 2 J or ^ in. per inch, 
or fir x T fiti 118 -! 1 J in. per foot. 



TAPERS AND TAPER TURNING 



156 



Problem 1 

Given the diameter of both ends of a piece of work, ana aiso 
the length. Find the taper per inch and per foot. 

Example. — Diameters |in. and fin., length 3J inches, 

as in Fig. 132. 

_, large diameter— small diameter . , 

Then ; n — ; n — : — r = taper per inch. 

length of work m inches * * 

Difference in diameter = g — $ = J. 

Taper in 3J inches = J. 

„ 1 inch J -f- 3J = A in. 

„ 1 foot = ^ x V '= }g = -923 inrh per foot. 

In this problem the length of the taper will have no effect 

on the taper per inch or per foot. In Fig. 133 the length can 

be taken from B to C, or A to D, without altering the taper 

por inch or the taper per foot. 




Fig. 133. 



SSL 



Problem 2 

Given the diameter one end, the length, and the taper per 
foot. Find the diameter of the other end. 

Example. — 1J inch large diameter, 4 J inches long, J inch 
per foot taper, as in Fig. 134. 

Then dia. large end — — j| x length of work) = 

dia. small end. 



156 



TAI'KltS AND XAPBB TURNING 



Taper per foot J in., taper per inch J H- 12 = ^ inch 

& x 4| = I inch. 
Dia. large end 1 J, then 1J — J = 1 inch dia. of small end. 
When the diameter of the small end is given, as in Fig. 135. 

Then dia. small end + P ei " P er ^ ] eng tb f wor k) m 

dia. large end. 

Taper per foot J in., taper per inch = J ~ 12 = X. 

iAt X 4$ = | in. 
Dia. small end + J = 1 J inch = dia. of large end. 



Fig. 134. 



-i 



W=\ 



Flo. 135. 
4C 



E 



TAPER 'A' PER FOOT 



Tape* H'perfoot 



Problem 3 
Given the diameter of both ends, and the taper per foot 
Find the length of the taper. 

dia. of large end -dia. of small end 

taper per foot--- 12 = len e fch of ta P er ' 

dia. of lar ge end— dia. of small end 

taper per inch ~ = ,en 6 th of ta P er - 

Example.— Large dia. 1^ in., small dia. Jg in., and -75 in. 
taper per foot, as in Fig. 136. 

Difference in diameters l^g — Jj{ = J = -25. 

Taper per foot '75. 

Taper per inch -75 — 12 = '0625. 

Then length in inches -25 -f- -0625 = 4 inches = length of 
taper. 

Fig. 18G. 



(& 



% 



TUnn 7S0~in& per foot 



TAPERS AND TAPKR TURNING 



157 



Skt-over of Tail-stock 

A common method of turning tapers on lathes not fitted with 
special taper-turning attachments is to set the tail-stock 
centre out of line with the head-stock centre. If the tail- 
stock centre is set over a distance equal to A in Fig. 137, 
and the work is turned with the tool moving parallel to the 
bed, then the difference in the diameters of the taper will be 
equal to 2 A. 

To find the set-over of the tail-stock centre, use the following 
formula : — 

Length of work in inches X taper per inch , 

— 5 s ~ — ■ = set-over of 

tail-stock. 



Fio. 137. 



— ~U3 



Q>— ■= 



Fig. 138. 
SI 



TaPEB%' PER FOOT. 



Example. — Length of work 6 inches, taper per foot f in., as 
in Fig. 138. Find amount of set-over. 
Then taper per inch = $ -r- 12 = ^5. 

Taper in inches = ^ X C = $j. 
Set-over of tail-stock = $j -j- 2 = g\ in. 
When both diameters are known, and work is turned its 
full length. 
Then (large dia. — small dia.) x £ = set-over. 



158 



TAPERS AND TAPER TURNING 



Example— large diameter 1$,, small diameter f jf, aa in 
Fig. 139. Find amount of set-over. 

Large dia. 1A small dia. 16. 

JA-H-S 

J X h = i = set-over. 
Pig. 139. 



% 



Fici. 140. 



A. 



If part of a piece of work is to be tapered. Example : 
Large diameter 1 J, small diameter f, length of taper 6 inches, 
total length 9 inches, as in Fig. 140. 
Then taper in 6 inches = J. 

Taper in 1 inch = § ~ 6 = ^. 

Tapor in 9 inches = ^ v 9 = ft. 

Set-over of tail-stock centre = A -^ 2 - A. 



Tapers per 


foot with 


Corresponding Angles. 


Taper 


Included 


Angle with 


Taper 


Included 






Angle. 


Centre Line. 


per ft. 


Angle- 


Centre Line- 


Ins. 






Ins. 






i 


0°— 36' 


0°— 18' 


1 


4°— 46' 


2°— 23' 


i 


1°— 12' 


0°— 36' 


1* 


7°— 09' 


3°— 35' 


A 


1°— 30' 


0°— 45' 


1? 


8°— 20' 


4°— 10' 


1 


1°— 47' 


0°— 54' 


2 


9°— 31' 


4°— 46' 


A 


2°— 05' 


1°— 02' 


2£ 


11°— 54' 


5°— 57' 


§ 


2°— 23' 


1°— 12' 


3 


14°— 15' 


7°— 08' 


J 


3°— 35' 


1°— 47' 


34 


16—36' 


8°— 18' 


H 


4°— 28' 


2°— 14' 


4 


18°— 55' 9°— 28' 






APPENDIX 

Useful Tables, Rules, and Notes 

Capstan and Turret Lathe Tools 

^■ $i_c/e Clearance 

Side sfi 
Clearance 




.Side Rah 



Side Clearance Front Clearance Side Clearance 



tint Clearance 





Metal 


Top 
rake 


Side 
rake 


Front | Side 
clearance : clearance 


Turning and facing 
tools 


Steel 

Cast iron 
Brass 


O 

12 

8 



12 

8 



o o 
12 12 

12 12 
12 12 


Parting tools . . . 

>> 


Steel 
Cast iron 
Brass 


12 
1 









12 
12 
12 


2 
2 
2 


Knife tools . . . 


Steel 





35 


8 


7 



Soldering 

Fluxes used in Soldering 

The flux prevents oxidization of the surface of the metal 
and facilitates the flowing of the solder. 

Fluxes used. 
Resin, Sal Ammoniac, Chloride of Zinc. 

Hydrochloric Acid dilute. 

Chloride of Zinc, Sal Ammoniac. 

Chloride of Ammonia. 

Tallow, Resin. 

Resin. 

Stearin. 



Name op Metal. 
Brass 
Copper 
Zinc 
Iron 
Steel 
Lead 
Tin . 
Aluminium 



160 



APPENDIX 






Soft Solders 
Composition. 

Tin. Lead. 
Fine . . \\ l 
Tinmans . 1 1 
Plumbers . 1 2 


Melting-point 
Degrees. 
334° F. 
370° F. 
440° F. 


Hard Solders 






Copper. Zinc. 
Hard . 3 1 

1 1 






Flux for Hard Solders 
Borax. 





Speed Calculation 

A simple rule for calculating the speed of shafts and the size 
of pulleys to give a required speed neglecting slip and thickness 
of the belt. 

Rule. — Multiply those two numbers together which belong 
to the same pulley, and divide by the third number, the result 
will be the answer required. 

The number of revolutions made by connected pulleys are 
inversely as their diameters. In other words the diameter of 
the driving pulley multiplied by the number of revolutions it 
makes per minute, is equal to the driven pulley multiplied by 
the number of revolutions it makes per minute. 

Therefore, to find the number of revolutions made by a 
driven pulley, if the diameter of the driver and driven pulley 
and also the number of revolutions per minute made by the 
driver are given. — 

Multiply the diameter of the driver by the number of 
revolutions per minute, and divide by the diameter of the 
driven pulley. 

Example. — Diameter of driving pulley, 12 in. ; diameter of 

driven pulley, 6 in. ; number of revolutions made by driver per 

minute, 120. Find speed of driven shaft. Then — 

12 x 120 
-g— = 240. 

Speed of driven shaft, 240 revs, per min. 

If the diameter of the driver, and the number of revolutions 
made by the driver and driven pulleys are given. To find the 
diameter of the driven — 

Multiply the diameter of the driver by the number of its 
revolutions per minute, and divide the result by the number of 
revolutions made by the driver. 



APPENDIX 



161 



8 Example.— Diameter of driving pulley, 18 in. ; number of 
revolutions made by driver per minute, 160 ; number made by 
driven, 120. Find diameter of driven pulley. Then — 

18 x 160 



120 



= 24. 



Diameter of driven pulley, 24 in. 

If the diameter of the driven pulley and the number of 

revolutions made by both the driven and driving pulley are 

given. To find the diameter of the driving pulley- 
Multiply the diameter of the driven pulley by the number of 

its revolutions, and divide by the revolutions per minute of the 

driver. 

Example.— Number of revolutions per minute made by the 

driving pulley, 60 ; number made by driven, 120 ; diameter of 

driven pulley, 20 in. Find diameter of the driving pulley. 

Then— 

20 x 120 

— 60~ = 4 °- 

Diameter of driving pulley, 40 in. 

Cone Pulley* 

To find the speed given by cone pulleys as attached to 
a machine tool. The illustration shows a three-step cone 
pulley driven from a countershaft running at 120 revolutions 
per minute ; the diameters are 8, 10, and 12 in. 



_ Shaft 120 . 
f- revs, per mm. 



To find the various speeds multiply the speed of the counter- 
shaft by the size of the pulley the belt is running on the 



162 



APPENDIX 



countershaft and divide by the size of the corresponding 
pulley on the machine. The various speeds would be : 

(1) 1*0x12 = 18Q 

(2) 120xl0 =120. 
' 10 

(3) 120X8 = 80. 

12 

Transmission of Power 

Belting. — To find the horse-power wine U can be transmitted 
by tingle leather belts. — Multiply the breadth of belt in inches 
by 70, and by the speed of belt in feet per minute ; and divide 
by 83,000. The quotient is the horse-power. 

Double belts transmit 1} times as much power as single 
belts. 

To find the loidth of tingle belt for transmitting a given 
korse-power. — Multiply the horse-power by 33,000, and divide 
by 70 times the speed of the belt in feet per minute. The 
quotient is the width of belt in inches. 

These rules are sufficiently approximate where there is no 
great degree of inequality in the diameters of the pulleys. 

Shaftino. — To find 'he horse-power which ean be trant- 
mittrd by a wrought iron shaft. — Multiply the cube of the 
diameter of the shaft in inches by the number of revolutions 
per minute, and divide by 80. The quotient is the horse- 
power. 

To find the diameter of a wrought iron shaft required to 
transmit a given horse-power. — Multiply the horse-power by 
80, aad divide by the number of revolutions per minute. The 
cube root of the quotient is the diameter in inches. 

ROPES. — To find the horse-potoer that ean be transmitted by 
ropes. — Multiply the sectional area of one rope in square 
inches by 100 times the speed of the rope in feet per minute, 
and divide by 33,000. The quotient is the horse-power for 
one rope. 

Or, multiply the sectional area of one rope by the speed, 
and divide by 830. 

TOOTHED Wheels. — To find the horse-power that can be 
transmitted by toothed wheels. — Multiply the velocity of the 
pitch- line in feet per second by the breadth of the teeth in 
inches, and by the square of the pitch in inches, and divide 
by 16. The quotient is the horse-power. 

For bevel wheels, the mean diameter and mean pitch are tx> 
b« Ukeu. 






TABLES 



163 



Px 



O.TJ 
II 1 



Sq, 



■*» -«~ 5 
6 *°S 

iili 



ft. ^^.fc. 



1 






Ifrj 



lONOQICrtHHfllHn 

■«*t~Oi5(N<- < O "5 CC lO OO 

gt-—>—icom'-"3>cci-'o 
*wn-ihhoooo 



COOt-OOCOCJOCJt-OCl 



goo 

to r- 



iCOt~O0COt--«ffl« 



toc~oO'-iooco'C^t<'*eo«o 
eo«—ii-<0000000 



IO O S) 8 6 W h H o o 

— <x <£> t- n — ooot-fflw 



H-HNM*OtOt«MOlO 



164 TABLES 

British Standard Whttworth (B.S.W.) 







Core 


Tapping 


Size. 


Pitch. 


Diameter. 


Drill 


Ins. 


t.p.i. 


Ins. 




rV 


60 


•0412 


57 


ft 


48 


•0670 


60 


I 


40 


•0930 


41 


| 


32 


•1162 


31 


i 
r 


24 


•1341 


28 


24 


• 1653 


18 


20 


•1860 


11 


a 


18 


•2414 


D 


§ 


16 


•2950 


N 


A 


14 


•3460 


S 


1 


12 


•3933 


X 


A 


12 


•4558 


H 


§ 


11 


•5086 


H 


n 


11 


•5711 


n 


i 


10 


•6219 


V 


h 


10 


•6844 


k 


i 


9 


•7327 


u 


H 


9 


•7952 


H 


i 


8 


•8399 


n 


|A 


8 


•9024 


Si 


14 


7 


•9420 


H 


A 


7 


1-0045 


i* 


l* 


7 


1-0670 


l? 


i& 


7 


11295 


iS 


if 


6 


1-1616 


m 


»A 


6 


1-2241 


m 


l| 


6 


1-2866 


m 


IS 


5 


1-3689 


it 


1J 


5 


1-4939 


if 


if 


4-5 


1-5904 


m 


2 


4-5 


1-7154 


m 


81 


4-5 


1-8404 


m 


2J 


4 


1-9298 


w 


2} 


4 


2-0548 


2A 


2$ 


4 


2-1798 


2A 


2§ 


4 


2-3048 


m 


H 


3-5 


2-3841 


m 


2J 


3-6 


2-6091 


m 


3 


3-6 


2-6341 


m 






TABLES 



Systemb International (S.I.) 



165 







Core 


Tapping 


Size. 


Pitch. 


Diameter. 


Drill. 


mm. 


mm. 


mm. 




2-5 


•45 


1-87 


49 


3 


•6 


2-16 


44 


3-5 


■6 


2-66 


36 


4 


•75 


2-94 


31 


4-5 


•75 


3-44 


28 


5 


•9 


3-73 


26 


5-5 


■9 


4-23 


18 


6 


1 


4-59 


t 


7 


1 


5-59 


8 


1-25 


6-24 


E 


9 


1-25 


7-24 


L 


10 


1-6 


7-89 





11 


1-5 


8-89 


T 


12 


1-75 


9-54 


W 


14 


2 


11-19 


Y 


16 


2 


1319 


u 


18 


2-5 


14-48 


u 


20 


2-5 


16-48 


H 


22 


2-5 


18-48 


II 


24 


3 


19-78 


27 


3 


22-78 


H 


30 


35 


25 07 


i 


33 


3-5 


28 07 


H 


36 


4 


30-37 


h\ 


39 


4 


33-37 


m 


42 


4-6 


35-75 


iff 


45 


4-6 


38-75 


m 


48 


5 


41-05 


iff 


52 


5 


45-05 


m 


56 


5-5 


48-36 


182 


60 


5-6 


52-36 


2A 


64 


6 


55-66 


m 



166 



TABLK8 



TABLF.S 



167 



British Standard Fine (B.S.F.) 



Cycle Engineers' Institute (C.B.I.) 









Core 


Tapping 


Size. 


Diameter. 


Pitch. 


Diameter. 


Drill. 




Ins. 


t.p.i. 


Ins. 




17 I.W.( 


3. -056 


62 


•0388 


No. 61 


16 „ 


•064 


62 


•0468 


„ 56 


15 „ 


•072 


62 


•0548 


., 54 


14 „ 


•08 


62 


•0628 


A in- 
No. 49 


13 „ 


•092 


56 


•0730 


12 „ 


•104 


44 


•0798 


2 mm. 


iin. -125 


40 


•0984 


2i „. 


•154, 


•154 


40 


•1274 


No. 30 


•175, 


•175 


32 


•1417 


„ 27 


1 : 


•1875 


32 


•1542 


„ 23 


•25 


26 


•2090 


„ 4 


•266, 


•266 


26 


•2250 


,, 1 


•281, 


•281 


26 


•2400 


C 


1 : 


•3125 


26 


•2715 


r 


, -375 


26 


•3340 


8J mm. 


A . 


•5625 


20 


•5092 


13 „ 


l 


1 


26 


•9590 


24J „ 


•1-29 , 


1-29 


24 


1-2456 


li in. 

Hi ,. 


1-37 , 


1-37 


24 


1-3256 


> : 


1-4375 


24 


1-3931 


35} mm. 


1-5 


24 


1 -4556 


37 „ 



For right-hand threads only. 



Size. 




Core 
Diameter. 



Tapping 
Drill. 



t.p.i. 


Ins. 


28 


•1731 


26 


•2007 


26 


•2320 


22 


•2543 


20 


•3110 


18 


•3664 


16 


•4200 


16 


•4825 


14 


•5335 


14 


•6960 


12 


•6433 


12 


•7058 


11 


•7586 


10 


•8719 


9 


•9827 


9 


1-1077 


8 


1-2149 


8 


1-3399 


8 


1-4649 


7 


1-5670 


7 


1-8170 


6 


2-0366 


6 


2-2866 


6 


2-5366 


5 


2-7439 



168 



TABLES 



TABLES 



169 



British Standard Pipe (B.S.P.) 



British Association (B.A.) 







Core 


Tapping 


Size. 


Pitch. 


Diameter. 


Drill. 


No. 


mm. 


mm. 







1-00 


4-80 


11 


1 


•90 


4-22 


18 


2 


•81 


3-73 


26 


3 


•73 


3-22 


30 


4 


•66 


2-81 


33 


6 


•69 


2-49 


39 


6 


•63 


2-16 


44 


7 


•48 


1-92 


47 


8 


•43 


1-68 


61 


9 


•39 


1-43 


53 


10 


•35 


1-28 


55 


11 


•31 


113 


56 


12 


•28 


•96 


61 


13 


•25 


•90 


64 


14 


•23 


•72 


69 


15 


•21 


•65 


71 


16 


•19 


•66 


74 


17 


•17 


•50 


76 


18 


•15 


•44 


77 


19 


•14 


•37 


bV 


20 


•12 


•34 


80 



Pipe 




Core 


Tapping 


Size. 


Pitch. 


Diameter. 


Drill. 


Ina. 


t.p.i. 


Ins. 




1 


28 


•337 


ii 


! 


19 


•451 


21 


1 


19 


•589 


M 


I 


14 


•734 




1 


14 


•811 


ft 


f 


14 


•950 


U 


i 


14 


1-098 


h\ 


1 


11 


1-193 


w 


U 


11 


1-634 


m 


1* 


11 


1-766 


m 


l| 


11 


2-000 


2A 


2 


11 


2-231 


H 


n 


11 


2-471 


m 


2J 


11 


2-844 


m 


H 


11 


3-094 


8A 


3 


11 


3-344 


33! 



Temperatures of Lead Bath Alloys 



Parts of Lead. 


Parts of Tin. 


200 


8 


100 


8 


75 


8 


48 


8 


39 


8 


28 


8 


24 


8 


21 


8 


19 


8 


17 


8 



















Melting Temp. F" 
560 
550 
540 
520 
510 
490 
480 
470 
460 
450 



170 



i S 

3 ,2 

a 

a — 

u 



Z - 



1 8 



TABLES 



e ' Q r. © ii — n © © co -r © c © © o o © so © >-« © — -: — :■ 

~ ~ '- r f 5 * 3° ?' ? ~ — '." ? '{' V -• T- '.-" • ".- : ' - : ' V ' ' ~ 

__; ii — >: r ?i ..- ii»T-tii. r ~ ii si ■; K — / l-91-ac ia 

3 ~ ■ ' — ' ' : i co co ..-. -z- if: © o i .- r — .ft © -r a v. — 






h'S$£?g3S^888S$??SSg$83k3S 






•.! 9 CO 0* 51 © CO © II -T © I- 1- © >ft CO © © I- Op -*©"»■© -I- © 

-r r- t % - © >ft ii 71 -T" r. t- x — oo © oi-c^coccc-n 

a'«N«fit-o- co i co ^ cW- co o co © ^ i- © uo oi 05 © i-i 
i— -. i- — ii 7i so -T .; i- x © n Bl»e 5J •.: ; 
.-■ — -• -■< ii ii u co 



^3SS23SSS?g£gS£3Sg283gg82fi 

^mc» vooi-c-*«-«''o -i — — «*c :ic. kc« ~ x a 
_ fr>i-piffiawissi-aO'ii -ft i- © oi " 






.•©i.-5 1-©©OJ©»©©01M©eO» — ©©»«-©COC»©© 

- 5 a jo b n o s c n 7 c x o n » I.- 5 1 - - 71 5 o n -- 5 
• — ^■•ri^oococji — Booi-TfiM^i- *. *<• 9 9 9 

ED .- rl rH Ol CN CO -* © I- © © H -r © 5 — 



« 00 .ft i_- y ii 71 7T p — i- .ft -i 2 ^ co — fly 9. i_- © 1- — © So 
■ — ~i ro ^r o © 1- © © <ii © — i- ~ ii — — 11 o © 05 01 i» 

,_ — — — 71 11 co — .- ■- 1 - •/> © -< co .ft t- 



_; — 11 co CO '■* © ot. a — © ^t © 1 - -r iC .- 1- =: — - - 11 - 



r * -* .ft © .ft x n 11 -T y; 1 - © •r x rr. -f © CO 11 00 © © CO t- -t 
(N f II — I.- -H- Ol — r-l IS .ft 5 CO Ol © •* t- $ — CO .ft 3 Co -T © II 
_; ' ii N ©1 CO •* © I- 00 © CO j- ■— i- CO © PS >- > b i 1 --- — r 

H Hi-f-ciwcai-TkictoaosS 



;•©©© — © © 00 1- I- © .ft 1- II 50 — 1 



:50i-i-©"5i-iiso — co-r©co — 9 . . . 

_ ■ T* CO CO "ft I;- © •— I! © .ft /.".ooopHva 

^- ii ei co co * o -c i- 00 — •'-. '-■ — b. ■'-. ii A< © o — 

„ _ _ II -I ;- 



1 - •£ ■; 
^r!ft©iioo©cii 



a^388$£3S3?8S8?8$£8£SS?8S8 

• ^COI OICOCO-CO© «-©II©© CI C©C0 — ©©« — CO 

_ 1- — -• 01 Ol co 9) -r .ft © © t- © © 



»!f|S8{!?88888888S?$?P?&88889 

-J .-« — CMUCOCO^^OCO©*:*- — O©©!!©/*© q-jas 

a " — — N II CO CO -t O u". ■- ,~3 



~ _^LT 



cciojicijici»nc3»T»TTiac*c)c3 



TABLES 



Weights of Flat Bar Iron 



171 



riiick- 



Inch. 



Thick, 
nan. 



[nob, 
I 



Width in Inenes. 



2J 8 S* 3i 3J 4 



Lbs. 

1 -Ml 

2-4H 
.•{•(ii) 
3-59 
4-19 
479 
5-39 
6-00 
659 
7-19 
7-79 
839 
x-'.is 
9-58 



Lbs. 
1-88 
2-50 
313 
3-7:. 
4-38 
5-00 
5*68 
6-25 
6-88 
7'SO 
s-i.'i 
s-7.-. 
9-88 
10-0 



Lbs. 
203 

2-71 

8-89 
1*06 

4-74 
5-42 

(j-nn 
6*77 

7-45 
8-L'i 
8-80 
9-48 
102 
10-8 



l.bs. 

8-66 

4-SS 
5-10 
5-83 
6-56 
7-29 
8-02 
s-7.-, 
9-48 
1 1 >2 
10-9 
11-7 



Lbs. 

813 
8*W 

Iti'.t 

5-47 
6-26 
7-08 

7-81 
8-59 
9-38 
10-2 
10-9 
11-7 
12-5 



Lbs. 
B*88 

•117 
5-00 
5-83 
6*67 

7-.MI 
833 
917 
10-0 
10-8 
11-7 
12*5 
18-8 



41 4J 



Lbs. 

3-54 
4-43 
5-31 
(l-L'd 
7*08 
7-97 
8*86 
;i-7t 
ki-i; 

11*6 

12-1 

18*8 

H-2 



Lbs. 

3"75 
4-69 
5-68 
6-66 
7*80 
,v-ll 
9*88 
10*8 
113 
12-2 
131 
111 
16*0 



*4 



Lbs. 

8-96 

4-95 
5-94 
6*98 
7-92 
8-91 
9-90 
10-9 
11*9 
12-9 
139 
11 -8 
15-8 



Lbs. 

11 T 

5-21 
8*26 
7-29 
8-33 
938 
10-4 
11*5 
12-r. 

13-5 
14-fi 

1 .->•(; 

n;-7 



Width in Inches. 



5j 


f» 


61 


7 


8 


9 


10 


11 


l.bs. 


Lbs. 


Lbs. 


l.b>. 


Lbs. 


Lbs. 


Lbs. 


Lbs. 


I'.-iS 


5*00 


f>-42 




6-«7 


■;■:.( 1 


8-83 


9-17 


5*78 


6*2S 


8*77 


7-2!' 


833 


'.'•:;- 


10-4 


11-5 


c.-ss 


7*80 


8-18 


S-7.*> 


10-0 


11-3 


12-r. 


18-8 


S-i)-.! 


s-7.". 


9-47 


10*2 


11-7 


18*1 


1 4f, 


16-0 


9-17 


10-0 


](i-.s 


11-7 


18*8 


15*0 


l(i-7 


1 8*8 


10*8 


11*8 


12-2 


181 


l.VM 


KJ-9 


18-8 


20-6 


11*5 


1 :••'. 


I8*S 


14*8 


16-7 


18*8 


20-8 


229 


12« 


13-8 


11-9 


16*0 


1 8-8 


20-fi 


22-9 


2.V2 


1 8-S 


18*0 


l.i-.-i 


1 7*8 


20-0 


22*6 


28*0 


27-r. 


14-9 


n;-:t 


17-6 


190 


21-7 


244 


27-1 


29-8 


ir.-n 


1 7-r. 


19-0 


2H-I 


28*8 


26*8 


292 


32-1 


17-2 


[8-8 


20-3 


21*9 


26*0 


28-1 


81*8 


34-4 


18-3 


20-0 


21-7 


28*8 


26-7 


30-0 


33-3 


367 



12 

Lbs. 

10*8 
12*5 

l.-.-n 
1 7-5 
20-11 
225 
25-0 

27-r, 

80-0 
32-5 
350 
37-5 
40-0 



172 



TABLES 






c 

§ 

B 

5 
Q 



© 
so 

o 

IS 

© 
© 

(M 

■o 

S 

IS ■** ' 

1*— 

£ 

■ 

P 3 

= g 
« 

o 
co 

o 
t- 

o 

to 

© 


_£ 
:(. 

- 

7. 
c 
g 

'C 

1 

— 
I 

1 
1 
\ 

H 

» 
I 

7 


a; oo xi oo »- to to is ■- •- -i — — — —■ oo oc is is 

_ — i SB is t" Ci CO '.- 7" 55 * CO ' - CO -- '- — © C-l 00 •* 
Jjj Ah •— — A. ^- CI CI CO CO CO -!• -r is is to t~ t- OC OC Ci 


is —< co -«■ -o n ci -p Ci ci to Ci -»• ci -r Ci ■+ oc eo oo 
-j A. « A, A- A- iji ci ci eb eb co ■# -r is ih to is t>- t» 


r! Ci CI 10 OC — 1 00 -f c; 10 CI Ci 10 C CO CO 7-1 i— i •— O -- 
•*" 1^ — 1 O — CO is oo — CO f X — MS ~. CO 1- — IS Ci CO 
p' ' 1 l«^rtfH 1 ^eN^CN0^COCOCO-^'-*iSiOlsi 


a; ai ; m •(• + ■/; - -tsr. co is o-i-oim«h*i- 

— oc ~ := — i co -o {- - ri >-. i - — 7" ';- -71 ■* 00 r-i in 

3j' ' ' ^ ,** ,h •*•< iH 01 ci 01 c» co co co ■* ■* 'f i"s ie 


-JciCiCiOiceaooot-t^tc to to © is is -*< -* eo eo eo 
is to 1- 00 cr. 1— co is ►»■ ci — • co — Ci ci •" 00 — « tc r- 

;f' ■" ' iiAi-rtNfieqsiKWM'ii'f-i 1 


r" Ci 1- © •# IN CO 10 — X -* O © Ol © r- IS O 3< CO IS 

" -c 10 » t~ 00 a — s: •+ '-o x c w •? 1- ci ci -* © ci 
pj A< A- Ai ih ^t ^ ©» ©» in oj co eb cb cb 


Si Ci <B 03 0) is — . 71 is rr — 10 1^- t~ sc t- 'O t0 ift •£ Mi 

co -r is 10 ^ 1— ci -* co -*■ is 1- ci -7 co ip b- 01 i-h 
53 Hrtrti-Hi-HMNN«(flK 


- • ,- _ 1- ~ —. — 1 co — ' ■- X c 01 C-. 1- 10 eo 00 «a »j 

— w -,. — ■ is is 1- X cs — co -r 10 t~ Ci — eo m< «p <» 

-j A-A"^H — — — — NMNMC4 


- ' S3 1 - M 1- Ol CO CO ~** iS "** IS '— Ol '- CO Ci "-*• -^ tO CO 
~" CO : CO t> — IS "C l~ OS Ci O — 1 0;1 — IS t^- SO p « CO >_5 


r! r. 01 1 1 - iS -+ CO CO 01 — 9 — 00 04 IS Ci CO to — 

Ol CO CO -f -*« iS to 1- X Ci ~ — Ol CO iS to 1- Si O 5-1 


— (llilHl-ltlHlll"!*-*-' 


n"o«coweicw«ii«oci»o:'Ci:»oo«iN 
?i oi oi co co co -r- is is to t~ r- x •— m eo "t 1 is 

ai ±~~^~- 


ll" 

IS 

- c 


-■M-f«oxc;-»-x s-i -o — cr — c s « « t e a 
-3— ,__- — c-ioiojco«0'*<-*''^ , >=tctot-t-»o'o> 



s 

1 

cc 



I 5-!- 



> s: c 



TABLES 

Weights of Flat Bab Iron 
Length, 1 foot 



173 





Width in Inches. 










ness. 


i 


8 


1 


I 


1 


H 


H 


10 


n 




luck 


Lbs. 


l.bs. 


| Lbs. 


Lbs. 


Lbs. 


Lbs. ' 


Lbs. 


Lbs. 


Lbs. 




A 


■sot 


-_'hi 


•312 


•866 -417 


■4691 


•621 


•573 


-626 




s 


•312 


■311 


-469 


■647 "626 


708 


•781 


•859 


-987 




i 


-117 


•683 


■626 


•72'.' -888 


•938 


101 


1 ' 1 5 


1-25 




A 


•521 


•66] 


■781 


'.111 1-0 1 


1-17 


1-30 


11:1 1*66 




I 


•621 


■78] 


•1)37 


1-09 


l-2.-» 


1-41 


1-56 


1-72 1-88 




& 


•72! 


•91] 


1-0'J 


1-28 


1-48 


1 6 1 


1-82 


2-01 2- 19 




i 


•s:i: 


l-oi 


1 -2.-. 


1-48 


1-67 


1-88 


2-08 


2*29 2-50 




ft 


•ll.T 


117 


Ill 


l-r.i 


1 -88 


211 


234 


2-58 2-81 




1 


MI4 


1-30 


1 •:.(; 


1 -82 


2-08 2-31 


2*60 


2*86 |3I3 




l« 


1-15 


I- 13 


1-72 


-.'•in 


2-211 2-68 


2-8H 


8*15 3-n 




1 


1*25 


1 •-)(*» 


1-87 


21'.' 2*50 2-S1 


313 


3-44 3-7.-. 




y 


1-8B 


1 •(!'.) 


2-08 


2-37 271 8-06 


3-39 


3-72 U-0(i 




2 


l-4f» 1*82 


2-19 


2-56 2-92 3-28 


3-tir. 


l(U 1-38 




if 
1 


lr.f, 1 •»."> 


L-.'M 


2-73 3-13 8-52 


3-111 


1-3.1 


l-Uit 




1-87 2'08 


2-60 


2-92 3-33 8-76 


4-17 


1*58 


5-00 






wi.ui. in Inehes. 










nen, 


1« 


13 


If 


•-' 


n 


2* 


28 


H 


2| 


2J 




Inch. 


l.bs. 


Lbs. 


Lbs. 


Lbs. 


Lbs. Lbs. 


Lbs 


Lbs. 


Lbs. Lbs. 




A 


•(577 


•729 


78J 


•888 








ft 


102 


1-09 


•17 


1 -2:. 


1-33 111 


1-41 


{•66 1*64 


172 




1 


L-85 


1-16 


•.-.c, 


1-67 


1-77 


1 >88 


1-91 


2-08 


2-19 


2-29 




2 


i-r,i» 


1*82 


•96 


2-08 


2-21 


2-34 


24 - 


2*61 


273 


2-86 




2-08 


-'■I'.i 


!-34 [2*50 


2-66 


2-81 


2-9' 


8-11 


3-28 


344 




7 


m 


2-58 


•7:t 2-92 


3-10 


328 


8-48 8-61 


3-83 


4-01 




I 


2-71 


292 813 J3-33 


8-64 


8-76 


3-91 


4-17 


4-88 


4-58 




ft 


3-05 328 8-62 


8-TH 


3-98 


4-22 


i-i: 


4-I5J 


4-92 


5-1 G 




1-89 8-66 8-91 


1-17 


4-43 


4-69 


4-9." 


5-21 


5-47 


5-73 






3-72 101 4-30 


4-58 


4-87 


5-16 


•VI 


57i 


6-02 


6-30 




l-Oli 


4-88 4 -69 


5-00 


581 


6-68 


6-9 


6*28 


6-56 


6-88 




15 
in 
1 


4-40 


4-74 . 


• ■08 


5-42 


5*76 


(•.•(Hi 


c.-i: 


671 


711 


7*48 




4-74 


510 5-47 


.VS." 


6-20 


6-66 


(;•*.•: 


7-29 


766 


8-02 




? 


r08 


3-47 6-88 


6-28 


6-64 7-03 


7-4f 


7-81 


8-20 


8-59 




:.-42 


-.-83 r.-2.-. ii-t!7 


7-08 7-60 7-9: 


s-X 


875 


917 








174 TABLES 

Metals Weights for various Dimensions 









Weight of One 


$ 








§ 


3 


Square Foot 




s 
















•J A 




Metal. 


a 
g 

I 

CO 


*5 

t! 




OS 

■3H 


ti 


►a 


11 
•so 






Wn.'glit 
Iron = 1. 


Lb. 


LI). 


Lb. | Lb. 


Lb. 


Lb. 




Aluminium, wrought 


•348 


167 


18-93 


1-74 1*89 1*160 


097 




„ cast . . 


•333 


160 


13-33 


1*67 


1-33 1-111 


092 




Antimony 


•879 


418 


84-8S 


4-35 


8*48 2-902 


242 




I'i.smulli . . . 


1-285 


617 


51-42 


6-42 


5-14 


4-283 


357 




Brass, cast 


1 -052 


505 


43-08 


5-26 


4-21 


8-507 


292 




„ sheet . . 


1*098 


527 


48*93 


5*49 


4-39 


3-652 


304 




,, yellow . 


1-079 


5 IS 


43-17 


5-4ii 


4-32 


3-597 


298 




„ Muntz metal. 


1-062 


511 


42-58 


5-32 


4-26 


3-549 


296 




„ wire 


1-110 


533 


44-42 


5*55 


4-44 


3-701 


308 




Bronze, gun-metal . 


1-108 


531 


44-25 


5-54 


4-43 


3-688 


307 




„ mill bearings . 


1133 


544 


45-33 


5-66 


4-53 


3-780 


315 




„ small bells 


1-00-1 


482 


40-17 


5-04 


4*02 


3-347 


279 




„ speculum metal 


•9(59 


465 


38-75 


4-84 


3-88 


3-299 


•269 




Copper, sheet . 


1-114 


549 


45*76 


5-72 


4-58 


3813 


•318 




„ hammered . 


1-1. 18 


556 


46-33 


fi-79 


4-68 


3-861 


■322 




„ wire . . 


1-164 


554 


46-17 


5-77 


4-62 


3-778 


•315 




Gold 


_'■:.<)( i 


1200 


100-00 


12-60 


10-00 


8-333 


■694 




Iron, cast . . . 


•937 


450 


87*60 


4-69 


3-75 


3125 


•260 




„ wrought . 


1-000 


480 


40-00 


5-00 


400 


8*888 


•278 




Lead, sheet . . 


1-483 


712 


69*88 


7-41 


5*98 


4-944 


•412 




Manganese 


1-040 


499 


41-58 


5-211 


4-16 


8*466 


•289 




Mercurv . . . 


1-769 


849 


70-75 


8-84 


7-07 


5-896 


•491 




Nickel, hammered . 


1127 


541 


45-08 


5-64 


4 51 


3-757 


•313 




„ cast . . 


1-076 


616 


43-00 


537 


4-30 


8-688 


•299 




Platinum 


2-79iI 


1342 


111-83 


13-97 


11-18 


11-320 


•777 




Silver . . . 


1-866 


655 


64*68 


6-82 


5-46 


4-649 


•379 




Steel 


1-020 


490 


40-83 


5-12 


4-10 


3-403 


•284 




Tin . . 


•962 


462 


38-50 


4-81 


3-85 


3-208 


•268 




Zinc, sheet 


•935 


449 


37-42 


4-67 


3-74 


3-118 


•260 




„ cast . . . 


•892 


428 


35-67 


4-46 


3-57 


2-972 


•248 








TABLES 176 

Vulgar Fractions of a Lineal Inch in Decimal Fractions 

Advancing by Thirty-second*. 



Thirty- 

Reeonds. 


Fractions. 


Decimals of 
an Inch. 


Thirty- 
seconds. 


Fractions. 


Decimals of 
an Inch. 


1 


tI- 


•03125 


17 


8 


•53125 


! 


s 


•0625 


18 


£ 


>5625 


I 


•09375 


19 


1 


•69875 


i 


■125 


20 


? 


•626 


8 


i 


15625 


21 


1 


■65625 


6 


& 


•1875 


22 


ft 


•6875 


7 


£ 


•21875 


23 




•71875 


8 


I 


•25 


24 


1 


•75 


9 


A 


•28125 


25 


■ 


•78125 


10 


1 


•3125 


26 


I 


•8125 


11 




•34375 


27 




•84375 


12 


I 


•375 


28 


¥ 


•875 


13 


1 


•40625 


29 


!» 


•90625 


14 


is 


•4875 


80 


1 


•9876 


15 




•46875 


31 


i 

i 


•96875 


16 


f 


'0 


32 


1-0 


Advancing by <u 


d Sixty-fourth*. 


Sixty- 




Decimals of 


Sixty- 
fourths. 




Decimals of 


fourths. 




an Inch. 




an Inch. 


1 




•015625 


35 




•546875 


3 




•046875 


37 




•578125 


5 




•078125 


39 




•609375 


7 




•109375 


41 




•«4C.)25 


9 




■140626 


43 




•671875 


11 




■171875 


45 




■708136 


18 




•203125 


47 




•734375 


15 




•234375 


49 




•765625 


17 




•265625 


51 




•796875 


19 




•296875 


53 




•828125 


21 




•328125 


55 




•859375 


23 




■359375 


57 




•890625 


25 




•390625 


59 




•921875 


27 




•421875 


61 




•953125 


29 




•458125 


68 




•984375 


31 




•484375 


64 




1*0 


33 




•515625 









176 TABLES 

Lineal Inches in Decimal Fractions of a Lineal Foot 



Lineal 
Inches. 


Lineal Foot. 


Lineal 
Inches. 


Lineal Foot 


Lineal 
Inched. 


Lineal Foot. 


A 


•001302083 


n 


•15625 


6^ 


•5416 


i 


•00260416 


2 


•1666 


H 


•5625 


ft 


■0052083 


2* 


•177083 


7 


•6888 


I 


•010416 


H 


•1875 


n 


•60416 


ft 


•01 562') 


2| 


•197916 


n 


•625 


i 


•02083 


*i 


•2083 


n 


•64583 


A 


•02604 16 


N 


•21875 


8 


•6666 


1 


03125 


88 


•22916 


H 


•6875 


ft 


•0364583 


23 


•239583 


H 


•7083 


1 


•0416 


3 


•25 


8| 


•72916 


ft 


•046875 


H 


•27083 


9 


•75 


1 


•052083 


H 


•2916 


91 


•77083 


tt 


•0572916 


8| 


•3125 


9i 


•7916 


1 


•0625 


4 


•3333 


H 


•8125 


a 


•0677083 


H 


35416 


10 


•8333 


i 


•072916 


*4 


•375 


m 


•85416 


*s 


•078125 


if 


•39583 


10^ 


•875 


i 


•0833 


5 


•4166 


103 


•89583 


ii 


•09375 


H 


•4375 


11 


•9166 


H 


•10416 


«4 


•4583 


11* 


•9375 


i| 


•114583 


5| 


•47916 


114 


■9583 


1* 


•125 


6 


•5 


111 


•97916 


it 


•135416 


6i 


•52083 


12 


1-0000 


if 


•14583 











TABLES 



177 



Tangents and Cotangents of Angles from 0° to 90° 
(Radius = 1.) 



Tangents 


Cotan- 




Tangents 


Cotan- 




of 


gents of 


Values. 


of 


gents of 


Values. 


Angle*. 


Angles. 




Angles. 


Angles. 







90 


•00000 


18-5 


71-5 


•33459 


r>0 


88*8 


•00873 


li) 


71 


•34433 


1 


89 


•1)1715 


19-5 


70-5 


•35412 


1-5 


88-6 


•0261'.' 


20 


70 


•36397 


2 


88 


•08492 


20-5 


69-5 


•37388 


2-5 


87-5 


•04366 


21 


69 


•383.SC 


3 


87 


•05241 


21-5 


68-5 


•39391 


8*5 


86-5 


•06118 


22 


68 


•40403 


4 


86 


•06998 


22-5 


67-5 


11121 


4-8 


85-5 


•07870 


23 


67 


12447 


.". 


85 


•087 l:i 


23-5 


tin-;. 


•48481 


5*8 


84-fi 


•09629 


21 


66 


•44523 


6 


84 


■10610 


24-5 


t;.v;, 


•45573 


6-5 


88*8 


•11891 


25 


65 


•46631 


7 


83 


■12878 


26-fi 


84*5 


•47698 


7*6 


S2-5 


■18188 


26 


64 


•48773 


8 


82 


•14054 


26-5 


(;:(•;. 


•49858 


8*6 


SI -5 


•14948 


27 


68 


•50952 


9 


81 


•15838 


27-5 


62*8 


•52057 


9-5 


80-5 


•16734 


28 


62 


•53171 


ID 


80 


•17688 


28-6 


61*5 


•54386 


10*5 


78*5 


•18531 


29 


61 


•55431 


II 


79 


•19488 


29>6 


60*8 


■56577 


1 1 -5 


78*8 


•20345 


80 


60 


•57735 


12 


78 


•21256 


80*6 


59*6 


•6890 1 


12-5 


77-5 


•22169 


31 


59 


•60086 


18 


77 


•23087 


31-6 


58-5 


•61280 


1S-5 


76-5 


•24008 


32 


58 


•62487 


11 


70 


•2 1933 


32-5 


57-.". 


•63708 


14-5 


71 "••") 


•25862 


33 


57 


•64941 


15 


75 


•26795 


33-5 


56*6 


•66189 


15"5 


74-5 


•27732 


84 


56 


•67451 


16 


74 


•28674 


31-5 


55-5 


■68728 


1 <;■.-. 


735 


■29621 


35 


55 


•70021 


17 


73 


•30573 


35-5 


5 1 -5 


•71329 


175 


72-5 


•31530 


86 


54 


•72654 


18 


72 


•32492 


88*5 


535 


•73996 






178 




TABLES 






Tangents 


Cotan- 




Tangents 


Cotan 




of 


gents of 


Values. 


of 


gents of 


Values. 


Angles. 


Angles. 
68 




Angles. 


Angles. 




37 


'75856 


57*6 


B2*8 


1 -56969 


375 


52-5 


■78768 


58 


32 


1-60033 


38 


52 


•781 1'9 


58-5 


31-5 


1-63185 


38-5 


61*6 


•79514 


59 


31 


1-66428 


39 


51 


•80978 


59-5 


30-5 


1-69766 


39-5 


50-5 


•82434 


60 


30 


1-73205 


40 


50 


•83910 


60*6 


29-5 


1*7671!) 


40-5 


49-5 


•85408 


61 


29 


1-80405 


41 


49 


•86929 


6T5 


28*8 


1*84174 


41", 


48-5 


•88472 


62 


28 


1-88073 


42 


48 


•90040 


62-5 


27-5 


192098 


42-6 


47*8 


•91688 


63 


27 


1-96261 


43 


47 


•932:. 1 


63-5 


26-5 


2-00569 


43-r, 


46-5 


•94896 


64 


26 


2-05030 


44 


46 


•9(5509 


64-5 


2.v:, 


2*09854 


44-5 


45-5 


•98270 


65 


85 


214451 


45 


45 


1-00000 


65*6 


24*6 


2-19430 


45*6 


■l-K. 


101761 


66 


24 


2*24804 


M 


44 


[•08558 


86*8 


88*6 


2-29984 


40*6 


48*6 


1-05878 


67 


23 


2*85586 


47 


43 


1 -0723 7 


67*8 


22-5 


2-41421 


47*5 


48*6 


1-09131 


68 


22 


2-475 Oil 


48 


42 


1-11061 


66-5 


21-5 


2*68886 


48*6 


41-3 


11 3029 


69 


21 


2*80609 


48 


11 


1-15037 


69-5 


20-5 


2-67162 


49-5 


40*6 


11 7085 


70 


20 


2-7-1 7 is 


50 


40 


1*19175 


70-5 


19-5 


2-82391 


60*6 


39-5 


1-21310 


71 


19 


2-90421 


61 


39 


1 -23490 


n*8 


18-5 


2-98K6S 


61*6 


38-5 


1*25717 


72 


18 


3-07768 


52 


88 


1*27994 


72-5 


1 7-:. 


8*17169 


525 


37-5 


1-30323 


73 


17 


3-27085 


53 


37 


1-32704 


73-5 


16-5 


3-37594 


B8'6 


88*6 


1-35142 


74 


16 


3-48741 


64 


88 


1-37638 


74-5 


15-5 


3-60588 


64*5 


85*8 


1-40195 


75 


15 


3-73205 


55 


35 


1-12815 


75*6 


14-5 


3-86671 


55*8 


34-5 


1-45501 


76 


14 


4-01078 


56 


34 


1*48858 


76-5 


13-5 


4-16530 


56-5 


33-5 


1 -.1084 


77 


13 


4-33148 


57 


33 


1-53986 


77-5 


125 


4-51071 









TABLES 

Tangents and Cotangknts of Angles 



179 



Tangents 


('iilaii- 




Tangent* 


Cotan- 


— ** — *™ 


of 


KenH Ol 


Values. 


of 


gents of 


Values. 


Angles. 


Angina, 




Angles. 


Angles. 




78 


12 


4-70463 


84-5 


5-5 


10-38540 


78-5 


11*5 


4-915 16 


85 


5 


11-4300.-. 


79 


11 


5*14465 


85-5 


4-5 


1270620 


79-5 


10-5 


5-39552 


86 


4 


14 30067 


80 


10 


5*67128 


si;-:, 


3-5 


16*84985 


80-5 


9*6 


5-97576 


87 


3 


19-08114 


81 


9 


6*81875 


87*8 


2-5 


22-90377 


81-5 


8-5 


6*89116 


88 


2 


28-63625 


82 


8 


7-11537 


88*6 


1-5 


38-18846 


88*5 


7-5 


7*59578 


89 


1 


5 7 -2899'! 


83 


7 


8*14485 


B9*S 


0-5 


114-58885 


B8*6 


t>-:> 


8-776*'.) 


90 





infinite. 


84 


6 


9*51486 









Lengths ok Circui 


jAB Arcs 


from 1° to 76° (Radius = 1) 


Dag. 

1 


Length. 


Deg. 


Length. 


Dag. Length. 


Deg. 


length. 


•0175 


20 


•8491 


39 


6807 


58 


Mil ■_'.-! 


2 


•0319 


21 


•8665 


40 


6981 


59 


10297 


3 


•0524 


22 


•3840 


41 


7156 


60 


1-0472 


4 


•0698 


23 


•lull 


42 


7330 


61 


1-0617 


5 


•0X73 


24 


■4189 


43 


7505 


62 


1*0821 


6 


•1047 


25 


•4888 


44 


767!) 


63 


1 -0996 


7 


•1222 


26 


•4688 


45 


7815 1 


64 


1-1 170 


8 


•1396 


27 


•1712 


46 


8029 


65 


1*1846 


9 


•1571 


28 


•4887 


47 


8208 


66 


1*1519 


10 


•1745 


29 


•.ml; | 


48 , 


8878 


67 


1*1894 


11 


• 1 920 


30 


•8286 


49 


8552 


68 


1*1868 


12 


•2(191 


31 


■84 1 1 


50 


8727 


69 


1*2048 


13 


•2269 


32 


•5586 


51 


8901 


70 


1 -22 1 7 


14 


•2113 


33 


•5760 


52 


9076 


71 


1 •2892 


15 


■2618 


34 


•5934 


53 


11250 


72 


1*2566 


16 


•2793 


35 


•6109 


54 


B 125 


73 


1-2741 


1 17 


•2967 


36 


•8288 


55 


9599 


74 


1-2915 


18 


•8112 


37 


•6458 


56 


9774 


75 


1-3090 


19 


•3316 


38 


•6682 


57 


9948 


76 


t*8285 



INDEX 



INDEX 



181 









Abbreviations, 2 
Abrasives. 147 
Accessories for lathes, 70 
Acme threads. 168 
Allowance for fits, 63 
Alloy steel. 37 
Alloys. 87. 13, 44. 45 
Allowance for contraction, 45 
Aluminium, 44 
Annealing. 46 

cast iron, 46 

copper. 47 

Angles of spirals, 1.48 
Antimony, 40 
Approximations, 102 
Area of surfaces. 22 
Artificial abrasives, 148 
Arithmetic, 1 
signs, 2 

B 
Back gear, 69, 70 
Belting, 150. 162 
Bench-work, 118 
Bessemer steel, 38 
Bevel gauge. 54 
Bismuth. 40 
Blast furnace, 35 
Blister steel, 39 
Bolts, 109 
Boring, 89. ill 

tools, 90 

British Association screws, 110,168 
British Standard fine threads. 
167 

Pipe threads, 169 

Bronze, 48, 44 



Calcining. 35 
Caliper gauges. 68 
Calipers, inside, 50 
micrometer, 56 

outside, 50 

vernier, 50 

Capstan lathe tools. 159 
Carbon. 37. 83 

ceinentite, 47 

pearlite. 47 

Case-hardening. 49 
Cast iron, 86 
Catching threads, 103 
Centre punch, 67 

stay, 71 

Change wheels, 95 
Chattering, 153 
Chisels, 118 
Chocks. 70 

independent, 70 



Chucks, self-centering, 70 
Circles. 23 
Circular pitch. 189 
Colours for tempering, 49 
Common denominator, 2 
Composition of alloys, 48 
Compression. 41 
Compound gears, 99 
Cone pulleys, 161 
Cones, 25 

Contraction of metals, 43 
Copper. 41 

alloys, 46 

Co-tangents, 170 
Cotter Mies, 120 
Crucible steel. 39 
Cubes. 24 
Cupola, 36 

Dg angle 79 
Cycle threads. 166 
Cylinders. 24 

D 
Decimal equivalents. 9. 176 

fractions, 7 

repeating, 9 

Denominator, 4 

common, 4 

least common, 4 

Depth gauge. 54 
Diametral pitch, 136, 139 
Dividend. 1 

Dividers, 51 
Dividing. 130 
Divisor. 1 

Drilling. 112. 111. 115 
Drills. Ill 
Ductility. II 

E 
Elastic limit. 41 
Elasticity, 41 
Ellipse. 24 
Elongation, 41 
Erecting machines, 147 
K>:p;uision, 42 

P 
KactorB. 1 
Feeds, drilling, 114 
planing. 128 

tools, 73 

turning, 73, 74 

Piles. 120 

Pits. 68 
Fitting. 118 
Flux. 159 
Formula, 17 
Fractions, 8 



Fractional pitch, 101 
Furnace annealing. 46 

Bessemer, 87 

blast. 35 

— open hearth. 39 
puddling, 36 



Fusibility, 42 



O 



Gas pipes, 111 
Gauges, depth. 54 

limit. 04 

radius. 53 

thickness, 68 

Gear cutting. 135 

Geometry. 22, 27 

Grade of grinding wheels. 149 

Grinding. 147 

wheels, 150 

H 

Hacksaws, 58 
Hammers, 118 
Hardening 47 

steel, 47 

Hardness, 42 

of grinding wheels, 149 

Heat treatment, 46 
Hematite, 33 
Hexagons, 25 
norse-powor. 162 



Improper fraction. 1 
Inch. 50 

Indexing, 130. 132. 183 
Inside calipers, 50 

micrometer. 62 

Integer. 1 

Internal threads, 89 
Iron. 84. 40 

malleable. 40 



pipes. Ill 

K 
Keys, 122 
Knife tools. 88. 93 



Lathe countershaft, 69 

speeds. 78 

tools, 78 

bathes, 67 

apron, 68 

back gear. 69 

chucks, 70 

face plate, 71 

gap, 67 

headstock, 68 

speeds. 78 

stays. 71 

surfacing. 68 



tools, 78 

Dead. 41 

Lead baths. 169 

of screws. 95 

Least common denominator, 2 
Leather belts, 153. 172 
Left-hand threads, 105 
Limit gauges, 63 

M 
Machines, milling, 125 

planing. 123 

shaping, 123, 124 

Malleable iron. 40 
Marking-off table. 53 
Materials, 34 
Measuring gauges, 64 

miorometers, 56 

rules, 50 

tools, 56 

vernier, 58 

Melting point metals, 44 
Mensuration, 22 
Metal, aluminium, 48, 44 
brass, 40 

brazing, 48 

gun, 48. 45 

white. 43, 45 

Metals, properties of, 41 

strength of, 41 

Micrometers. 06 
Milling. 125 

cutters, 127 

speeds, 128 

Mixed number, 1 
Multiple threads. 104 
Multiplicand, 1 
Multiplier. 1 

N 
Nickel. 41 

Non-ferrous metals, 40 
Numerator. 1 
Nuts, 110 



u 

Open hearth furnace. 89 
Operations of milling. 125 

planing, 128 

shaping. 124 

turning. 67 

Outside calipers, 51 



Parting tools, 88 
Percentage, 2, 16 
Pin punch, 62 
Planing. 123 
Polygons. 25 
Precision grinding, 147 
Prime numbers, 1 
Product, 1 



182 

Properties of metals. 11 
Proportion, 15 
Protractor. CI 
Puddling furnace, ."Hi 
Pulleys. 70, 161 
Punch. 52 
Pyramid, 25 



INDEX 



Quotient, 1 



Q 



B 



Radius gauge. 53 
Ratio. 2, 97 
Reciprocal. 2 
Repeating decimal. 9 
Rhombus, 22 
Round-nose chisel, 119 
Rules. 50 
Running fits. 63 



Scrapers. 121 

Screws, 108. 109.110, 111 

Screw-cutting, 94 

gauge, 55 

Scribers. 52 
Scribing block, 54 
Shafting. 170 
Shear steel, 37 
Shearing strength, 44 
Side tools. 88 
Signs, arithmetical, 2 
Soldering. 148 
Solids. 26 

Specific gravity, 42 
Speeds of drilling. 113. 114 
milling, 123 

planing, 123 

pulleys. 70. 101 

shaping, 134 

turning. 7:1 

8phere. 24 
Spiral angles. 142 
Spur gears, 185 
Standard rule, 50 

yard, :t 

Steel alloys, 87 

annealing. 16 

Bessemer, 38 

blister, 39 

crucible, 39 

high speed .37 

mild, 37 

open-hearth, 39 



pipes. 111 

Strength of metals, 41 
Surface gauge, 54 
plate, 53 

T 

Tables. 163 
Tangents, 178, 179 
Taper gauge, 66 
Tapers, 158 
Tapping, 112 

gauge, 55 

Taps, 116, 117 
Temperature table, 48 
Tempering, 47 
Tenacity, 43 
Tensile strength, 42 
Thickness gauge, 58 
Threads, 94, 95 

multiple, 101 

Tin, 41 

Tool design, 82 
Toughness, 42 
Transmission of power. 162 
Trapezoid, 22 
Try square. 52 
Turning tapers. 155 
Turret lathe tools, 159 
Twist drills, 114 



Ultimate strength metals, 44 
Universal dividing head, 180 



Vanadium, 38 
Vee blocks. 53 

threads. 108. 109 

Vernier, 58 

caliper, 00 

Vices, 118 

w 

Water annealing, 47 

for grinding, 151 

Weight of metal. 45. 164. 166. 174 
Wheels, grinding. 151 
Whitworth taps. 117 

threads. 108. 109 

Wire gauge, 55 
Wrought iron. 34, 40 



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